Iterate.

Hello Math-Fun,

Here is another stupid iteration – which leads nowhere, probably.

This in “p”; now make the absolute differences between p’s digits, from left to right, like this:

1-9    = 8

9-5   = 4

5-1  = 4

1-1 = 0 (this is the last digit of “p” minus the first one)

You then get “q” = 8440.

And now: if q > p add q to p and iterate

If q < p subtract q from p and iterate.

Here:

1951

+  8440

-------

10391  step 1

+ 13680

-------

24071  step 2

+ 24761

-------

48832  step 3

- 40512

-------

8320  step 4

- 5128

------

3192  step 5

- 2871

------

321  step 6

- 112

-----

209  step 7

+ 297

-----

506  step 8

+ 561

-----

1067  step 9

+ 1616

------

2683  step 10

+ 4251

------

6934  step 11

- 3612

------

3322  step 12

- 101

------

3221  step 13

- 1012

------

2209  step 14

- 297

------

1912  step 15

+ 8811

-------

10723  step 16

...

Etc.

Don’t know where this goes: zero? Infinity? Loops? Fixed points? Patterns? Errors above? Waste of time? (yes!)

Best,

É.

__________

October 10th 2012 update.

[Hans Havermann]:

1951 yields:

{1951, 10391, 24071, 48832, 8320, 3192, 321, 209, 506, 1067, 2683, 6934, 3322, 3221, 2209, 1912, 10723, 28235, 94358, 43127, 30974, 70205, 142457, 464583, 243232, 32122, 21021, 9810, 8091, 17078, 84795, 41552, 7520, 5193, 331, 309, 705, 1457, 4583, 3232, 2121, 1010, 2121, ...}, so {1010,2121}, a small loop.

There are loops of assorted lengths but a difficulty in compiling them is that even some small numbers (like 199 which apparently loops to {30,63}, if I’ve done this correctly) take their time in getting to them:

I have added an asterisk (*) beside the maximum number to make it easier to find.

[Eric]:

[Hans Havermann]:

It’s the evolution of the number 199 using your procedure. The left column numbers are the step numbers:

199      <- step 0

808 +

1007     <- step 1

1076 +

2083     <- step 2

etc.

So, all I’ve done with that file is show that it takes 12940 steps to reach a number that has been previously encountered, which is how we determine a loop.

[Eric]:

ok, thanks Hans (...)

[Jean-Marc Falcoz]:

Je viens de regarder un peu cet algorithme. J’obtiens les mêmes résultats que Hans en partant de 199. La plupart des nombres terminent leur parcours relativement rapidement, mais il semble y avoir un tas d’entiers dont la trajectoire s’étend sur 13000 itérations (un peu moins, ou un peu plus pour certains).

Parmi ces entiers, 199, 924, 1007, 1220, 1387, 1389, 1434, 1441, 1446,... (par exemple, la première itération pour 924 donne 199, qui est lui-même très long).

(...)

__________

In examining Hans’ link, we see that 199 enters in the (small) loop {30,63} after 12940 steps, reaching its maximum “altitude” at step 5091 which is... 4355844064496136145565824445826790824724344584482457236782364726952, a 67-digit figure, waow!

But this is nothing compared to the following examples.

Here are the last of the 43559 steps of 10853 – which enters also in the {30,63} loop:

(...)

`43530 106454`
`43531 268567`
`43532 691682`
`43533 306418`
`43534 668793`
`43535 647530`
`43536 415294`
`43537 71544`
`43538 7441`
`43539 4405`
`43540 3954`
`43541 10365`
`43542 23679`
`43543 10552`
`43544 25583`
`43545 55934`
`43546 51323`
`43547 9211`
`43548 2103`
`43549 972`
`43550 715`
`43551 73`
`43552 29`
`43553 106`
`43554 271`
`43555 832`
`43556 316`
`43557 63`
`43558 30`
`43559 63`

The maximum “altitude” of 10886 was:

`18602 47268036226040834444456790454609106572346054596959`
`      08487910306723525680492790044707236054556969192569`
`      62805044566787970784675907`

... which is a 126-digit integer!

Here are the last of the 67626 steps of 10886 – which enters also in the {30,63} loop:

`67598 197`
`67599 1023`
`67600 2235`
`67601 2112`
`67602 1102`
`67603 981`
`67604 803`
`67605 1638`
`67606 6995`
`67607 3954`
`67608 10365`
`67609 23679`
`67610 10552`
`67611 25583`
`67612 55934`
`67613 51323`
`67614 9211`
`67615 2103`
`67616 972`
`67617 715`
`67618 73`
`67619 29`
`67620 106`
`67621 271`
`67622 832`
`67623 316`
`67624 63`
`67625 30`
`67626 63`

67618 73

67619 29

67620 106

67621 271

67622 832

67623 316

67624 63

67625 30

67626 63

The maximum “altitude” of 10886 was:

`25747 93456789926804456703096084569029727849283696704945`
`      02470650848926808796792628269636934556804694240306`
`      72844496369007 `

... which is a 114-digit integer.

The red figure 3954 (in the last two examples) shows the possibility that an integer has more than one predecessor. The study of such predecessors would be of interest too, I guess.

Thanks again to Hans and Jean-Marc for their good work!

__________

October 15th 2012 update.

[Hans Havermann]:

(Note the file sizes.)

I’ve run into a number whose outcome is unknown, so I decided to highlight the fact by blogging about it: http://gladhoboexpress.blogspot.ca/2012/10/13094.html

I have just updated the blog entry with a graph up to ten million iterations. I would not have predicted such a dedicated upward climb. The largest number herein exceeds 13000 digits.

Many thanks, Hans – impressive work – and (logarithmic) graph of 13094!

We see here that 13094 has transformed, after ten million iterations, into a monster integer of more than 13000 digits! – Will it collapse and enter into a cycle? Who knows!

[Phil Carmody]:

> ...They all enter soon or later in a loop -- except 13094 which seems to... fly forever!

Indeed - 13 million iterations, 17000+ digits...

13359679[17564]: 1002790403901636585004064300636454565454345656765357888480544000200366037706250803566

010506241201536364544552486934355565677064063030792940188456805440064563364545585064567899667667576789

906406484476100384801796758036482330906575570323605431565559506925660006480240358004566024304004021057

900303696784554859033065657000160564756567045032584566038472460278479050630231703801612069685458024366

846507838357078885760000108556023249256200648934720032484644028720603656767595557694320306456012036571

032789658478954030370063210293678989879686412206233658400803645449630402925455565832583204024306472036

484828403800231203656870294504032206242064300644456568231404062324580365646355960300120244546002312018

100040310232056063636492565675823123159687241250301878992760192840365787984056027876570324558503224056

565956965565902249256469558454566002435245456706302790064544536480245679063800223456770302243460064444

824486778790016336206584000244805595660007725684445456559204790404900200290802455832567658470072020068

860636232046024567559508021648602436160304080380106574233637032008204545430184064536365685443584556608

020067658315668900603660403660400907206970069253624356031064935761300163064545656047702312058240302944

565656545689896243567906584002935001247247896965003255575801789263360400240003768003903236363344815695

4467684370790436013450803903653545657580364565040648172822322925 [... thousands of other digits]

It’s crunching away an a merry old fashion on an otherwise unused machine, so I can let it run... Unfortunately, I only log when it grows to a new maximum, or when it reaches <13094, so it might get stuck in a limbo with no logs. However, as it’s logging merrily away presently, that’s not a concern.

e.g. since I wrote that paragraph, it’s got to this level:

14330578[19198]: 1100120294570447022321248030494324054363685456403901886078104455647702456464044454559

344470807685445658224488010836018854560706090719404722410198402232243456845456039014424787024406702393

602324723236676966880004559803920087008057044006832003901885574242343501876567104566885029357880289246

493604565916687032806038445565604558365028630469667678756464057045018854345455700563592705839249029384

070293450706462242348073022240249019583430359243457050456045604566881615047032003003844445457019360475

843457070179656007003106806242304454445650187844465598370300300357698240846684482322835038249030417870

187648240816696045696901984940400542314697037001966968048054407302503670195655967045567036702884608045

670648241788925363668454480444544564800007702936767878240080724334223246360805568453696871017900410584

055981024400108488370304685744454566960723360770566868696847917028546867695824250544024304559360719494

490445356486944345599190905363033028856569032444824035169701970223244559168840320090292781045479080446

076776710240036686944545605432569248684552046455844824236030643456846075600769463226090720544445360717

236029440447501902448060008036454475007686241019203656756024382434056005810458405556581029449024470805

726970222433600200178856480015248816570639016125065045570390367232567839367717029095600559359582480879

9279160037443470190294490048447170292454569040400200294906702390 [...]

And I see another log’s appeared already...

Make that nearly 75 million iterations and over 100000 digits:

74274818[103019]: 107028484756536564700303000128029702002456685659029434570224004642006850302854545594

024459046002945450 [...]

[Hans Havermann, quoting Eric A.]

> 13094... seems to be the smallest integer escaping gravity.

I had assumed that a plus and a minus were equiprobable but, empirically, I’m finding that a minus may actually be more probable than a plus, at least for small numbers. This helps keep things down. However, the long-term evolution of 13094 argues strongly that, on average n becomes a number greater than n, and the eventual downfalls in the evolution of 199, 10853, and 10886, are the exceptions, not the rule.

__________

October 25th 2012 update

[Phil Carmody]:

Now stopped, at >150M iterations and >210000 digits.

Final state available here for posterity:

(other intermediate logs will be culled quite soon, as they’re big)

I noticed with the logs that went past that the digit pair ‘56’ seemed unusually common. So I grabbed some stats on digit distribution. Sure enough, ‘56’ was 3.17x as common as you’d expect from a uniform distribution. More so, ‘456’ was 9.23x as common as you’d expect. That’s what the distribution file is in the above directory. These are clearly not random numbers. I’ve not yet checked to see if the distribution for terminating numbers is different from seemingly-non-terminating numbers? Are there seeds of non-terminal doom inside the non-terminating ones, subsequences that are guaranteed to never collapse? Alas, I don’t think I have time to look into that any more, but I think someone else should be able to do that instead.

Here’s some out-of-the-{box,arse} thinking: Is this somehow like a cellular automaton? Have we discovered something Wolfram would have wet dreams about?

All data, and the code I posted elsewhere, can be considered in the public domain.

[Hans Havermann, quoting Phil C.]

> Is this somehow like a cellular automaton?

When looking at long stretches of large numbers evolving, the most obvious visual impressions are from repdigit patterns, because these will propagate for a bit before they die. On their own, repdigits are of course length-one cycles.

(...)

Just a heads-up on the fact that I’m still working on this and likely will be for another month or so. First, I’ve put up a cycle list.

I’ve also written a general purpose program that looks for long loops, long runs that end in a cycle, and ‘escapes that are not known to end in a cycle. The program is relatively slow but still better than anything I’d written up to now, mostly because it automatically excludes extension/variant evolutions that I was previously having to determine manually.

I’ve only just run this for a day. The only long loop found is the length-25 one that I already had in my cycle list. For long runs that end in a cycle, in addition to 199, 10853, 10886, I now have files (in the ‘asi’ folder) for 13391, 13864, 16385, and 16523. For possible escapes, in addition to 13094, I now have 13837, 16076, 18686, 20864, and 27650. Assuming that these are all actually different, I’ll attempt to document them at some point in the future.

__________

October 29th 2012 update

[Hans Havermann]:

I now have a second long loop and it's a good one: length 868!

Many thanks, Hans; here is this nice 868-long loop, with the longest integer (21-digit) marked by a star at step 572:

0 204099163

1 449007694

2 389936344

3 900569445

4 1805704459

5 9658444607

6 6524441935

7 5204403314

8 1963973083

9 10300216935

10 23602370559

11 9980895512

12 9792755095

13 7517549151

14 5055390705

15 10558088455

16 25596892559

17 56029065606

18 39749453945

19 102104580457

20 223245964583

21 212031643232

22 99706432122

23 96944321015

24 63443209871

25 32431918706

26 20303046943

27 43636470454

28 30304096344

29 63649029445

30 30389754434

31 63901964545

32 26983643434

33 70136854546

34 141369165667

35 473707676683

36 128936566432

37 290567668543

38 1085678691654

39 2916791076767

40 10768072787882

41 27896827898943

42 79029479010454

43 49754149896341

44 101967501029474

45 220280012304807

46 197599900959932

47 1020000810400543

48 2240009524805655

49 1999915199954552

50 10000760000365583

51 20007920003675935

52 40080640036800558

53 80966880369605592

54 170268963703256068

55 842690298434572695

56 418297584323318352

57 41575243213043120

58 7352032089630996

59 3119719276291965

60 1037031761503653

61 2384357916036775

62 843135059705752

63 430909516953516

64 290915063531064

65 1090760695752686

66 3087927037986911

67 6900684380110713

68 2994442799093090

69 10044468009057082

70 20444696108584943

71 44447031291930454

72 44409709503296344

73 43916914971563244

74 27063079707432044

75 84696802480544446

76 42363979995444424

77 21027759954444204

78 9777519544441962

79 7775035444403615

80 7749714443970073

81 7397084427699329

82 2769244176393157

83 7906447790055582

84 4944417499555217

85 10444781003558380

86 24447952035593961

87 4415519715127610

88 4075037070976096

89 8800384850193028

90 7996840498329768

91 5964395983157647

92 1642751830736415

93 6867999368168759

94 4655993040647516

95 2551929594415064

96 5600704044760686

97 3992959641594465

98 10070402876044677

99 20844828992446783

100 49249490064467934

101 106505080684680544

102 268060966926965647

103 696730270670276882

104 365297694497764818

105 51576343977640043

106 7363227776399631

107 3032177762796305

108 6343777908029657

109 3229774919756536

110 2157739037545303

111 737269695432972

112 291836354315717

113 1079369565558382

114 2805703675593943

115 9658436796060454

116 6524305559396339

117 5202955512763276

118 1975555097631765

119 10195561018957879

120 22035712190379007

121 19713100296949932

122 102335203030500543

123 223358436366005655

124 213124303059954552

125 91002969519543522

126 9975635035431215

127 9754309714310071

128 7542917083099303

129 5415049229192969

130 4069592150315635

131 8704063603556956

132 6959429971543544

133 3514159707431442

134 1080716934308421

135 2968370545692631

136 10293845657066952

137 23059256784670383

138 9511945642496832

139 5103434419964315

140 972324039643075

141 721199676429351

142 210396564153105

143 96765440730952

144 65654393291515

145 54542731507074

146 43417306929343

147 32052943153232

148 19515430732121

149 103956568143231

150 240367695454351

151 483679036565592

152 30549705455120

153 65702456559243

154 52980345512030

155 15797235099695

156 58022361003039

157 19821009969675

158 101432100302799

159 214543203628007

160 83431970159932

161 32303698719316

162 20970387033063

163 50243904336694

164 102460845367045

165 224729257684459

166 201151936444312

167 411600568445522

168 105995444435220

169 260036444558241

170 720368445594472

171 197044435144117

172 1024444559447183

173 2244445604483935

174 2044433964027312

175 4444540288281522

176 4443397681607220

177 4432776405932196

178 4317763951320364

179 3057627509197044

180 6579080108024445

181 5349198919804434

182 3190387037964323

183 296869695643213

184 1029103036854334

185 2307236369165347

186 932103030653212

187 320969694532095

188 191636343319153

189 1076969453607575

190 2790304577279799

191 8083645782802006

192 16936857949624068

193 70569180503048695

194 145707966036491037

195 458480272369072383

196 323997721029320832

197 207977209753192321

198 480182501976063432

199 961946020192694544

200 603419798318343439

201 1234802013593454602

202 119979891132341981

203 39758710921203811

204 101990330632439513

205 220083366944603935

206 199233063441967312

207 1006336694480281523

208 2069367044962955835

209 4705684450310359358

210 954444297097113124

211 544441569171090999

212 444407430509091995

213 443934294909103954

214 427321538910967544

215 173207287091655444

216 814482905076756447

217 84014949365544416

218 39879393055444064

219 101006056556448685

220 212072567568490919

221 99319455443891032

222 93034354428709715

223 29723144166917071

224 102235447670784832

225 222356478847929343

226 221144168415153232

227 210840644070732122

228 92394439293321022

229 20744271533209815

230 48046835734501558

231 96469358146015592

232 64233120819875115

233 42130992038751074

234 20891919687509344

235 49080802900105446

236 108969630801256468

237 290302969612568695

238 1083630303125691038

239 2936963635257072395

240 10570296958584824038

241 25843030391929448395

242 59256364080704494038

243 11943039192963939685

244 3429670315627276451

245 2156497074171764309

246 743969340505642912

247 427633194954415097

248 176330339544069174

249 789363403648707807

250 673031970406935937

251 529703695943311296

252 156970351433109565

253 570243594535303679

254 298031143312970555

255 1016351453530245558

256 2169594575762455595

257 635143353620355152

258 310833130197150718

259 92330898370693043

260 21292782894329627

261 9517616743156172

262 5056065430740515

263 10572676568085955

264 25826787696920359

265 59467899030643606

266 14256789694429945

267 46567903044700459

268 25454969640996314

269 56570302890029546

270 45296976699755425

271 31563766397554194

272 7429662775540343

273 4156617755397229

274 746057552772154

275 419535517720741

276 35315057193408

277 13069530331923

278 36703763360635

279 4969632994313

280 10302950045534

281 23630400455747

282 10295996353412

283 23040029574723

284 9599755341212

285 5197553210095

286 375532099155

287 795745007557

288 553429935537

289 532159315295

290 320713071555

291 193089307553

292 1056905679575

293 2570856803799

294 5849169638006

295 2390636279945

296 694301759432

297 342985514318

298 215855083043

299 72549229632

300 19392156317

301 106063569583

302 272695703935

303 827038440558

304 169684395528

305 702926035895

306 1430672359037

307 4566823608383

308 3464209922832

309 2241919216321

310 2003032063210

311 4036344694322

312 8369447045424

313 3034409634200

314 6344902946403

315 3238975423970

316 2087754207697

317 4897966479022

318 775664149820

319 754640798193

320 542393580329

321 420731197155

322 193310370754

323 1053523847967

324 2575839280283

325 5799406962934

326 3593943615323

327 1127430073213

328 974299332091

329 741593319103

330 407133030969

331 883336370304

332 833302896960

333 332976763592

334 315765631121

335 73654311009

336 30543109917

337 65655300781

338 54552993606

339 43515929945

340 31071159434

341 9310714323

342 3093083207

343 7056934481

344 14570544957

345 45845650383

346 32434496832

347 20323964321

348 43440285432

349 32397654320

350 20776543197

351 47787656022

352 17676539820

353 78787801441

354 67675988405

355 56551883954

356 45504827543

357 34960175432

358 19598554321

359 104011565431

360 248115676551

361 1074565510

362 2805675921

363 9656800632

364 6543994315

365 5427943074

366 4175429343

367 554153232

368 540732119

369 393321035

370 1053432357

371 2574543583

372 5805655934

373 1954551323

374 10365593435

375 23676054559

376 10559543512

377 25603655923

378 57236760634

379 32105594323

380 20955143213

381 50359454334

382 103604565345

383 237245677459

384 92034574312

385 19723343095

386 102233457039

387 222334584407

388 221323243932

389 209212027322

390 506324281422

391 1069446954625

392 2704470367059

393 8444843684606

394 4440430441944

395 4396296403444

396 2761563972444

397 7915700224446

398 5072998204425

399 10830014444655

400 29360144446759

401 105721444468006

402 258234444696071

403 594344447032832

404 143244409716319

405 454444902369607

406 344438981035934

407 244287809711323

408 41675917109212

409 6551050912100

410 5509491100994

411 4913910991943

412 10740730080454

413 28088160964567

414 96895730285682

415 64753297654415

416 41531576544074

417 7307365439344

418 2933054273241

419 10536566814472

420 25767669544823

421 57878703649434

422 36766970394323

423 5663696743213

424 4630365432091

425 2297054319108

426 1569543030922

427 5703656370623

428 2970542894211

429 10245669046312

430 22456708469523

431 20344924235212

432 43450646358322

433 32294423123220

434 21544211012197

435 7442109900372

436 4420918996917

437 4191047963054

438 309615629544

439 703157103645

440 1435583236857

441 4555934369183

442 3551323030432

443 1509209696321

444 6106503029431

445 944969754306

446 439637542943

447 276295415432

448 791036756542

449 509705545417

450 1102455656779

451 980354545751

452 797143433503

453 570832330969

454 292321291635

455 1063433076958

456 2694536790395

457 7045768084038

458 14457896928389

459 44579030693907

460 43349694326934

461 33196343183324

462 30363230433203

463 63694364534433

464 30343043324330

465 63456453445363

466 32344332433030

467 21243320329697

468 10033197156372

469 20336023569823

470 43372235701434

471 32922112988324

472 15221095883203

473 58233038934435

474 22129687324315

475 20956473203072

476 50368814436822

477 103689544569425

478 236903645704659

479 102970432962512

480 230244550305923

481 98043496951212

482 79631963510095

483 56303631099153

484 42970309190731

485 15696910293308

486 57030723053695

487 29693209530355

488 103054503763558

489 236566037895595

490 105459696755152

491 256603027959583

492 567236280403934

493 452101595967323

494 320987151653212

495 191870706532101

496 1079048467743211

497 2808492678054311

498 9693066796565512

499 6329465565455095

500 3154255454349154

501 741954343190743

502 403543230293429

503 835654363054704

504 314543029540960

505 83429755391597

506 32157552707176

507 20735516930563

508 48155970565694

509 751695454344

510 506354343241

511 1069565454475

512 2703676564799

513 8436787688006

514 4305676479944

515 2954564159444

516 10365687604446

517 23676899244471

518 10564792044110

519 25688064447121

520 56896684483232

521 44766444032119

522 41664439721034

523 6644277209724

524 6441771917202

525 4405703051978

526 3952969503764

527 10390304037885

528 24083648378919

529 48936893790806

530 7304729491944

531 2961153903441

532 10311580834472

533 23515969344823

534 11071633240212

535 9306331998101

536 2943303980983

537 10453640170134

538 24576881841347

539 3364804409212

540 3039963912101

541 6400300723213

542 3996993212090

543 10030054325083

544 20360565460935

545 43725676730558

546 29194565295524

547 108045679035846

548 296456808359271

549 1028569693606832

550 2291703057269343

551 1504969531833232

552 6050303759334343

553 12603638005345456

554 27236996057456571

555 82370032580567832

556 20899719195456316

557 49002408036569570

558 108024896367703844

559 296249029678439247

560 1030508302792606482

561 2366093628067268943

562 1059130159451847432

563 2607361604599280543

564 7281717246006965654

565 1605052019943654541

566 7260584200456765671

567 1795241996345654505

568 8038480029456766059

569 16392960304567872600

570 70070323645679027201

571 140843436856808282417

572 489254569169694944783 *

573 71943430636339441632

574 3432294303274406317

575 2321542971743943053

576 1207415705427429532

577 2480758456680703743

578 4967992566968438054

579 10280065670292596564

580 22960676843066027687

581 15594564429459776472

582 56045684704601788823

583 39634440961985688211

584 102944490320116894313

585 230445083441169045535

586 96429232410629635312

587 64152120094156313095

588 40720999140743089154

589 88250007488056907564

590 81899934079542935440

591 4799319355415314392

592 1593033154073082720

593 6056335568816948241

594 12569355689570494476

595 25705556903845044791

596 58455570839260448072

597 24355292271796399319

598 3151521705562793032

599 707204955417529721

600 1482450356779902237

601 4944603567800822383

602 10447235679609423934

603 24482356803304640547

604 4021143972962395412

605 8231460230304036724

606 2108198096959705200

607 920379163516951998

608 196950631063503987

609 1030406952696040103

610 2364870387032481235

611 1040696869720010112

612 2487029102240121123

613 69750981999011012

614 37491803989909898

615 81079640100901013

616 9356398990989888

617 3142787891878887

618 817676704768873

619 56564961648728

620 45439606407165

621 34275943930654

622 21751427294543

623 5508171543432

624 4920507432319

625 10646080543604

626 26872965657247

627 69030276782482

628 29697765620018

629 103017877040194

630 236178984482047

631 100567844019612

632 205679248203123

633 456806494435234

634 343943944312124

635 227427443101003

636 174174430989972

637 807804570100223

638 1679645841202238

639 6802859272422395

640 3976511720220754

641 10187918242247965

642 21900794462480279

643 2993544219997752

644 10055646400017982

645 20556868800180143

646 45569089601961454

647 35429275983608344

648 14151751829923243

649 47597999500634455

650 15175994994324354

651 59800050045445567

652 17999499634435455

653 80005002944556559

654 160060030445567600

655 720720364455679201

656 193197044354551985

657 1056024445565600119

658 2572244455677201207

659 5822444556782412482

660 2220443545620100019

661 2196431434198999832

662 364308320387998322

663 42923196875983221

664 15210364751832208

665 58323687999342495

666 23210475993219955

667 12096151932039552

668 25031600544403583

669 60357205644835934

670 123582456849360546

671 11220344392995421

672 10197242715954211

673 22022468360366311

674 19820242997063110

675 101442470024695121

676 214464840247039231

677 84240398009672110

678 41996779916521092

679 3965759065209120

680 10278008678507243

681 22796090792082455

682 17559093519220352

683 79609056006243583

684 55909539942031229

685 50915279419710155

686 110758804802321555

687 93527959981207551

688 31175519809935503

689 10555037919314973

690 25560380805550215

691 55723969655602358

692 53207636553981125

693 31936305527810995

694 3302955176091953

695 2975550559103533

696 10195605607235734

697 22037257282358147

698 19691931621120812

699 103080557031249523

700 236965584352503835

701 103655243118968312

702 236758455190293523

703 105524350297531212

704 255845603019752323

705 559257236201983434

706 511932101983832323

707 103320983828321211

708 233450139493432311

709 132298873932321110

710 343009020543431121

711 229909795432311009

712 158917554321109912

713 590779565431300723

714 93755454308993211

715 29554342927932103

716 103565470680543234

717 235676846965654347

718 114564423654543212

719 83444210543432101

720 32442095432320984

721 20419154321191843

722 44807565432079254

723 39935454319351944

724 100556565605600445

725 205567677257204459

726 455678782582444606

727 354567619220441944

728 143456032196403443

729 454572344028834455

730 343321239768324354

731 233210077643203143

732 132099376431970832

733 345005788560249343

734 229953685397993233

735 159530452775932132

736 603764587800543343

737 1237885899605653456

738 96852795954532341

739 64517551543321203

740 43055507433209970

741 29554934331919696

742 103570545360803030

743 235845657729636361

744 112434537156303010

745 100323290742969899

746 203435088070301007

747 434560896843612082

748 323392764430099220

749 212717644299192197

750 97056441590320372

751 69544407097196915

752 35443929170363074

753 14427150497029343

754 44683605024305455

755 42429949802954354

756 20159397975543144

757 41606020195655446

758 5939798354554424

759 1277583143544203

760 2779935455646435

761 7800556556868558

762 5995545544645527

763 1955435442435175

764 10356556464559799

765 23567568685602007

766 11455446453979932

767 8354424327759321

768 3144203177513204

769 841970575091963

770 403695349103628

771 837037507237092

772 289694932089116

773 903050544907170

774 1836605650883849

775 9367256808939307

776 3051943927272935

777 6600460682830557

778 5996194416295536

779 1960344061555305

780 10323448715557659

781 23434490355578807

782 12323897155367932

783 1208770753055321

784 2489847976557431

785 78415765534310

786 64073655323093

787 39330553209130

788 105365574507363

789 257675806081695

790 578799672957038

791 367596515529685

792 55165075156453

793 50649350744331

794 106905608045355

795 270857296457559

796 849183028579606

797 390429765355944

798 1084701877560445

799 2928418979724459

800 10692790202244606

801 27068082422447271

802 84696944624482832

803 42363442204016316

804 21032421959863064

805 9720203518629442

806 7197971046154415

807 375709620744073

808 798503048048813

809 584969599608089

810 239635195919275

811 76310351031752

812 63097109705517

813 29170916955056

814 107850770360570

815 279207843725841

816 806479258259272

817 1668806594606828

818 6689668047269495

819 6476639611833954

820 4166276104327542

821 661760963175420

822 605591630554194

823 1256076965568046

824 2572790275696471

825 5828082797028832

826 2159217569768319

827 712055437643032

828 99554296429717

829 95541564157055

830 55407440729551

831 53934393155507

832 27322730754935

833 81428167970558

834 8160655695528

835 594554355168

836 143543150645

837 455655606859

838 354553944514

839 143527443083

840 455880456935

841 352796343314

842 117563233083

843 55432129231

844 54320952107

845 43191520935

846 30307191314

847 63684073545

848 30439331434

849 64605354545

850 41953143434

851 3530832324

852 1292321203

853 3063432435

854 6694544557

855 6343443536

856 3232431306

857 2120308943

858 996927432

859 963174315

860 630543071

861 295429306

862 1036705670

863 2368456841

864 1044344410

865 2445444721

866 434441210

867 324410096

868 204099163  (same term as the first one on the list)

__________

Update, December 30th, 2013.

Thanks to Jim Nastosscript, I’ve played with integers like 9a9b9c9d9e... See how 9192939495 enters into a short loop after 915 steps:

> 9192939495   - 8877665544

= 315273951   - 243546442

= 71727509   - 66552592

= 5174917   - 4635862

= 539055   - 269500

= 269555   + 434003

= 703558   + 732031

= 1435589   + 3120318

= 4555907   - 1004973

= 3550934   - 2059611

= 1491323   + 3582112

= 5073435   + 5741120

= 10814555   + 18731004

= 29545559   + 74110047

= 103655606   + 133101665

= 236757271   - 131225561

= 105531710   + 150226611

= 255758321   + 302235111

= 557993432   - 22061113

= 535932319   - 224611284

= 311321035   - 202111322

= 109209713   + 197292622

= 306502335   + 361521022

= 668023357   - 28210221

= 639813136   - 361722230

= 278090906   + 518999964

= 797090870   - 227998177

= 569092693   - 139974362

= 429118331   - 278075023

= 151043308   + 441410387

= 592453695   - 472123340

= 120330355   + 123033204

= 243363559   - 210332047

= 33031512   - 3324411

= 29707101   + 72776111

= 102483212   + 122451111

= 224934323   - 25611111

= 199323212   + 806111111

= 1005434323   + 1051111112

= 2056545435   + 2511111123

= 4567656558   - 1111111034

= 3456545524   - 1111110321

= 2345435203   - 1111123231

= 1234311972   - 1111208251

= 123103721   - 112134510

= 10969211   + 19337100

= 30306311   + 33363202

= 63669513   - 33034423

= 30635090   + 36325993

= 66961083   - 3351853

= 63609230   - 33697136

= 29912094   + 70812952

= 100725046   + 107535425

= 208260471   + 286464361

= 494724832   + 553524512

= 1048249344   + 1446256103

= 2494505447   + 2551551035

= 5046056482   + 5426512463

= 10472568945   + 14353121514

= 24825690459   - 24631394147

= 194296312   + 852733211

= 1047029523   + 1437274312

= 2484303835   - 2441335523

= 42968312   - 27325212

= 15643100   + 41212101

= 56855201   - 12303214

= 44551987   - 1048113

= 43503874   - 12535130

= 30968744   + 39321301

= 70290045   + 72790412

= 143080457   + 313884126

= 456964583   - 113321351

= 343643232   - 113211111

= 230432121   - 134111111

= 96321010   - 33111119

= 63209891   - 31291185

= 31918706   - 28871763

= 3046943   + 3423510

= 6470453   - 2374123

= 4096330   + 4933034

= 9029364   + 9276325

= 18305689   + 75351218

= 93656907   - 63113972

= 30542935   + 35127622

= 65670557   - 11175021

= 54495536   - 10540231

= 43955305   - 16402351

= 27552954   + 52037412

= 79590366   - 24493301

= 55097065   - 5927610

= 49169455   + 58535101

= 107704556   + 170741015

= 278445571   + 514010261

= 792455832   - 272103515

= 520352317   - 323231262

= 197121055   + 826111504

= 1023232559   + 1211113048

= 2234345607   - 111111675

= 2123233932   - 1111106610

= 1012127322   + 1111154101

= 2123281423   - 1111673211

= 1011608212   + 1105686111

= 2117294323   - 1065751111

= 1051543212   + 1544111111

= 2595654323   + 3441111111

= 6036765434   + 6331111112

= 12367876546   - 11311111125

= 1056765421   + 1511111210

= 2567876631   + 3111110321

= 5678986952   - 1111123433

= 4567863519   - 1111232485

= 3456631034   - 1110321311

= 2346309723   - 1123392511

= 1222917212   - 1007865111

= 215052101   - 145531111

= 69520990   - 34329096

= 35191894   - 24887151

= 10304743   + 13343312

= 23648055   - 13248503

= 10399552   + 13604031

= 24003583   + 24032351

= 48035934   + 48324610

= 96360544   - 33365105

= 62995439   - 47041163

= 15954276   + 44412515

= 60366791   + 63301285

= 123668076   - 113028715

= 10639361   + 16366350

= 27005711   + 57052601

= 84058312   - 44535216

= 39523096   + 64313933

= 103837029   + 135547278

= 239384307   - 166541375

= 72842932   - 56427615

= 16415317   + 52342266

= 68757583   - 21222353

= 47535230   - 32223134

= 15312096   + 42212935

= 57525031   - 22335324

= 35189707   - 24712774

= 10476933   + 14313602

= 24790535   - 23295223

= 1495312   + 3542211

= 5037523   + 5342312

= 10379835   + 13421524

= 23801359   - 15812247

= 7989112   - 2118015

= 5871097   - 3161922

= 2709175   + 5798623

= 8507798   - 3570210

= 4937588   + 5642304

= 10579892   + 15221171

= 25801063   + 33811631

= 59612694   - 43514351

= 16098343   + 56915112

= 73013455   - 43121102

= 29892353   + 71171221

= 101063574   + 111632233

= 212695807   - 114343875

= 98351932   - 15248617

= 83103315   - 52130243

= 30973072   + 39243751

= 70216823   + 72152614

= 142369437   + 321335146

= 463704583   - 234741351

= 228963232   - 61331110

= 167632122   + 511311101

= 678943223   - 111511013

= 567432210   - 113110115

= 454322095   - 111102941

= 343219154   - 111188411

= 232030743   - 112337311

= 119693432   - 83361111

= 36332321   - 33011112

= 3321209   - 111296

= 3209913   - 1290820

= 1919093   + 8889962

= 10809055   + 18899504

= 29708559   + 72783047

= 102491606   + 122585665

= 225077271   - 35705561

= 189371710   + 716466611

= 905838321   + 953555118

= 1859393439   + 7346661168

= 9206054607   - 7266512672

= 1939541935   + 8664138624

= 10603680559   + 16633285048

= 27236965607   + 55133311675

= 82370277282   - 61472505666

= 20897771616   + 28120065554

= 49017837170   + 59161546674

= 108179383844   + 187626555403

= 295805939247   + 743854667235

= 1039660606482   + 1363066662461

= 2402727268943   + 2425555421511

= 4828282690454   - 4666664394110

= 161618296344   + 555576733103

= 717195029447   - 666845275030

= 50349754417   + 53152210362

= 103501964779   + 132518323028

= 236020287807   - 136222611875

= 99797675932   - 2221124617

= 97576551315   - 22211042244

= 75365509071   - 22310599766

= 53054909305   - 23515996350

= 29538912955   + 74251817403

= 103790730358   + 134297433237

= 238088163595   - 158807532443

= 79280631152   - 27686320435

= 51594310717   - 44451217662

= 7143093055   - 6313963502

= 829129553   - 678174025

= 150955528   + 459400367

= 610355895   - 513203141

= 97152754   - 26435215

= 70717539   + 77662262

= 148379801   + 345421810

= 493801611   + 565815503

= 1059617114   + 1543566033

= 2603183147   + 4632752335

= 7235935482   - 5124621465

= 2111314017   - 1002234165

= 1109079852   - 199721331

= 909358521   + 996233318

= 1905591839   + 8950487568

= 10856079407   + 18316725476

= 29172804883   + 78656844051

= 107829648934   + 171673241613

= 279502890547   + 524526195135

= 804029085682   + 844279831266

= 1648308916948   + 5245381853547

= 6893690770495   - 2163397074541

= 4730293695954   - 3432763344410

= 1297530351544   + 1722233244103

= 3019763595647   + 3182132441234

= 6201896036881   - 4217136332075

= 1984759704806   + 8143242744865

= 10128002449671   + 11168022053160

= 21296024502831   - 11736221526521

= 9559802976310   - 4041827213219

= 5517975763091   - 462222133984

= 5055753629107   + 5502223478172

= 10557977107279   + 15022206175528

= 25580183282807   + 30381751666875

= 55961934949682   - 4358615553263

= 51603319396419   - 45630286632384

= 5973032764035   - 4243315124320

= 1729717639715   + 6572661362644

= 8302379002359   - 5321429021241

= 2980949981118   + 7189550170076

= 10170500151194   + 11675501440853

= 21846001592047   - 17426014472435

= 4419987119612   - 380116083512

= 4039871036100   + 4361161335104

= 8401032371204   - 4411311461244

= 3989720909960   + 6112529990363

= 10102250900323   + 11120359903112

= 21222610803435   - 11004518831123

= 10218091972312   + 12178988251211

= 22397080223523   - 1627882012311

= 20769198211212   + 27138816101110

= 47908014312322   - 32988131211102

= 14919883101220   + 35881052111021

= 50800935212241   + 58809623110234

= 109610558322475   + 193515035102324

= 303125593424799   + 332130461223206

= 635256054648005   - 323316512248051

= 311939542399954   - 208664121600411

= 103275420799543   + 131521227204112

= 234796648003655   - 113230248033103

= 121566399970552   - 114103600275031

= 7462799695521   - 3245203340316

= 4217596355205   - 2162433203251

= 2055163151954   + 2504532448412

= 4559695600366   - 1043341603302

= 3516353997064   - 2453226027621

= 1063127969443   + 1632152335012

= 2695280304455   + 4343683340103

= 7038963644558   + 7351333201031

= 14390296845589   + 31692732410318

= 46083029255907   - 26853277304973

= 19229751950934   + 87072248459613

= 106302000410547   + 163322004315136

= 269624004725683   + 433424043531251

= 703048048256934   + 733448446313613

= 1436496494570547   + 3132532551275136

= 4569029045845683   - 1139279413411251

= 3429749632434432   - 1272353312110111

= 2157396320324321   - 1424633123121111

= 732763197203210   - 415132825231117

= 317630371972093   - 261333468252960

= 56296903719133   - 14733934688202

= 41562969030931   - 34147339339623

= 7415629691308   - 3341473382381

= 4074156308927   + 4733413381753

= 8807569690680   - 872133396288

= 7935436294392   - 2621134751675

= 5314301542717   - 2231314125662

= 3082987417055   + 3867113367502

= 6950100784557   - 3451107141021

= 3498993643536   - 1511063212233

= 1987930431303   + 8112634122332

= 10100564553635   + 11105121023324

= 21205685576959   - 11251230213447

= 9954455363512   - 410102332417

= 9544353031095   - 4101223321944

= 5443129709151   - 1012172798444

= 4430956910707   - 139413817773

= 4291543092934   - 2784113977610

= 1507429115324   + 4573278042123

= 6080707157447   + 6887776423031

= 12968483580478   + 17324452384317

= 30292935964795   + 32777624323242

= 63070560288037   - 33775162608341

= 29295397679696   + 77742621123334

= 107038018803030   + 177358170833331

= 284396189636361   + 641635713333351

= 926031902969712   - 746328927332617

= 179702975637095   + 622727221347944

= 802430196985039   + 822131833135361

= 1624562030120400   + 5421142331124401

= 7045704361244801   + 7412741351204816

= 14458445712449616   + 30134012612053556

= 44592458324503170   - 1472135121532674

= 43120323202970500   - 12123111227275504

= 30997211975694990   + 39025108221355090

= 70022320197050080   + 70201121827550890

= 140223442024600960   + 342011022222609340

= 482234464247210300   - 460110222235113300

= 22124242012097024   - 1122222112927222

= 21002019899169800   - 11022181108531802

= 9979838790637998   - 221551296342011

= 9758287494295988   - 2236613552744101

= 7521673941551887   - 2315146534047010

= 5206527407504877   - 3261353472544102

= 1945173934960775   + 8514646615367024

= 10459820550327800   + 14141625053151800

= 24601445603479600   - 22613011631323600

= 1988433972156000   + 8104106251416001

= 10092540223572000   + 10973142012252000

= 21065682235824000   - 11611260123624002

= 9454422112199998   - 5110201011800011

= 4344221100399987   - 1102010103600113

= 3242210996799874   - 1220119031201131

= 2022091965598743   + 2202988310411311

= 4225080276010054   - 2035882516110510

= 2189197759899544   - 1718820241104102

= 470377518795442   - 373402471241022

= 96975047554420   - 33225432010229

= 63749615544191   - 34353540103885

= 29396075440306   + 76636721043364

= 106032796483670   + 166315232453171

= 272348028936841   + 551148261632431

= 823496290569272   - 611534795137556

= 211961495431716   - 108353541126654

= 103607954305062   + 133672411355641

= 237280365660703   - 145683311067731

= 91597054592972   - 84427511477257

= 7169543115715   - 6534112042642

= 635431073073   - 321121743743

= 314309329330   - 231396176033

= 82913153297   - 67822421721

= 15090731576   + 45997424215

= 61088155791   - 51807402285

= 9280753506   - 7687222563

= 1593530943   + 4462239512

= 6055770455   + 6502074101

= 12557844556   + 13021401015

= 25579245571   + 30227210261

= 55806455832   - 3862103513

= 51944352319   - 48501231284

= 3443121035   - 1012111322

= 2431009713   - 2121092621

= 309917092   + 390867971

= 700785063   + 707135634

= 1407920697   + 3472726326

= 4880647023   - 4086237211

= 794409812   - 250491715

= 543918097   - 116878922

= 427039175   - 257368621

= 169670554   + 533175013

= 702845567   + 726410110

= 1429255677   + 3277301106

= 4706556783   - 3761011151

= 945545632   - 510111317

= 435434315   - 121111241

= 314323074   - 231113731

= 83209343   - 51296115

= 31913228   - 28821065

= 3092163   + 3971530

= 7063693   + 7633364

= 14697057   + 32327526

= 47024583   - 37221351

= 9803232   - 1831117

= 7972115   - 2251042

= 5721073   - 2511742

= 3209331   - 1296022

= 1913309   + 8820398

= 10733707   + 17404776

= 28138483   + 67254451

= 95392934   - 42677615

= 52715319   - 35642284

= 17073035   + 67743324

= 84816359   - 44753241

= 40063118   + 40632074

= 80695192   + 86344876

= 167040068   + 517440627

= 684480695   - 240486341

= 443994354   - 16051210

= 427943144   - 252512300

= 175430844   + 621138403

= 796569247   - 231137230

= 565432017   - 111112162

= 454319855   - 111281301

= 343038554   - 113353011

= 229685543   - 73230111

= 156455432   + 412101111

= 568556543   - 123011112

= 445545431   - 10111123

= 435434308   - 121111384

= 314322924   - 231107721

= 83215203   - 51143235

= 32071968   - 12768325

= 19303643   + 86333212

= 105636855   + 151332304

= 256969159   + 313338447

= 570307606   - 273371661

= 296935945   + 733624513

= 1030560458   + 1335164137

= 2365724595   - 1312521443

= 1053203152   + 1521232431

= 2574435583   + 3230120351

= 5804555934   - 3841004611

= 1963551323   + 8332042112

= 10295593435   + 12740461124

= 23036054559   - 13336511047

= 9699543512   - 3304112417

= 6395431095   - 3641121941

= 2754309154   + 5211398412

= 7965707566   - 2312772101

= 5652935465   - 1137621210

= 4515314255   - 1442232301

= 3073081954   + 3743878411

= 6816960365   - 2753363311

= 4063597054   + 4632427510

= 8696024564   - 2336221124

= 6359803440   - 3241831046

= 3117972394   - 2062251651

= 1055720743   + 1502527312

= 2558248055   + 3036248503

= 5594496558   - 450531033

= 5143965525   - 4316310330

= 827655195   - 651104843

= 176550352   + 611053231

= 787603583   - 111632354

= 675971229   - 124261073

= 551710156   - 46611411

= 505098745   + 555911310

= 1061010055   + 1651110504

= 2712120559   + 5611125047

= 8323245606   - 5111211662

= 3212033944   - 1112306501

= 2099727443   + 2902553011

= 5002280454   + 5020684111

= 10022964565   + 10207321114

= 20230285679   + 22132631127

= 42362916806   - 21347852862

= 21015063944   - 11145636502

= 9869427442   - 1235253027

= 8634174415   - 2313630343

= 6320544072   - 3125104754

= 3195439318   - 2841166275

= 354273043   - 212543410

= 141729633   + 336573302

= 478302935   - 315327621

= 162975314   + 547222233

= 710197547   - 611822130

= 98375417   - 15421362

= 82954055   - 67414503

= 15539552   + 40264031

= 55803583   - 3832352

= 51971231   - 48261124

= 3710107   + 4611174

= 8321281   - 5111677

= 3209604   - 1293641

= 1915963   + 8844332

= 10760295   + 17162744

= 27923039   + 52713367

= 80636406   + 86332462

= 166968868   + 503320227

= 670289095   - 172619941

= 497669154   + 521038410

= 1018707564   + 1171772123

= 2190479687   - 1894323215

= 296156472   + 735412350

= 1031568822   + 1324120601

= 2355689423   - 1201215211

= 1154474212   - 410332111

= 744142101   - 303321116

= 440820985   - 48629131

= 392191854   + 671887311

= 1064079165   + 1624728514

= 2688807679   + 4200871127

= 6889678806   - 2013110860

= 4876567946   - 4111112522

= 765455424   - 111101223

= 654354201   - 111212215

= 543141986   - 112338121

= 430803865   - 138835211

= 291968654   + 788322112

= 1080290766   + 1882797105

= 2963087871   + 7333811161

= 10296899032   + 12732109311

= 23029008343   - 13279085111

= 9749923232   - 2350711117

= 7399212115   - 4607111042

= 2792101073   + 5271111741

= 8063212814   + 8631116734

= 16694329548   + 50351174147

= 67045503695   - 17410533341

= 49634970354   + 53315273210

= 102950243564   + 127452212123

= 230402455687   - 134422101215

= 95980354472   - 44183210357

= 51797144115   - 46226303040

= 5570841075   - 278431720

= 5292409355   - 3772496200

= 1519913155   + 4480822404

= 6000735559   + 6007420043

= 12008155602   + 12087401621

= 24095557223   + 24940025011

= 49035582234   + 59320360110

= 108355942344   + 185204521103

= 293560463447   + 762164231035

= 1055724694482   + 1502522350461

= 2558247044943   + 3036237405511

= 5594484450454   - 450440154111

= 5144044296343   - 4304402733112

= 839641563231   - 563234131127

= 276407432104   + 512473111142

= 788880543246   - 100085111221

= 688795432025   - 201241112231

= 487554319794   - 412011282250

= 75543037544   - 20113342103

= 55429695441   - 1273341034

= 54156354407   - 13413210472

= 40743143935   + 47312316621

= 88055460556   - 8501265012

= 79554195544   - 24013840103

= 55540355441   - 143201034

= 55397154407   - 2626410472

= 52770743935   - 35077316620

= 17693427315   + 61361254244

= 79054681559   - 29512274042

= 49542407517   + 54122472463

= 103664879980   + 133024120181

= 236689000161   - 130219001551

= 106469998610   + 162230012511

= 268700011121   + 421700100111

= 690400111232   - 394401001114

= 295999110118   + 744008011076

= 1040007121194   + 1440076110853

= 2480083232047   + 2480851112435

= 4960934344482   + 5369611100462

= 10330545444944   + 13035111005503

= 23365656450447   - 10311112154035

= 13054544296412   + 23511102732311

= 36565647028723   - 31111237261510

= 5454409767213   - 1110492115122

= 4343917652091   - 1116861132983

= 3227056519108   - 1057511488185

= 2169545030923   - 1534115339711

= 635429691212   - 321273381114

= 314156310098   - 233413210915

= 80743099183   + 87313908755

= 168057007938   + 528527072657

= 696584080595   - 331344885441

= 365239195154   - 313168844411

= 52070350743   - 32773257312

= 19297093431   + 87727961120

= 107025054551   + 177235511040

= 284260565591   + 642465110481

= 926725676072   - 741531116757

= 185194559315   + 734851046244

= 920045605559   - 720411650040

= 199633955519   + 803306400488

= 1002940356007   + 1027543216076

= 2030483572083   + 2334452252851

= 4364935824934   - 1325623625610

= 3039312199324   + 3366211806121

= 6405524005445   - 2450324051011

= 3955199954434   + 6404800410111

= 10360000364545   + 13360003321114

= 23720003685659   - 14520033231147

= 9199970454512   - 8800274111417

= 399696343095   + 603333113942

= 1003029457037   + 1033275127346

= 2036304584383   + 2333341341551

= 4369645925934   - 1333214734610

= 3036431191324   + 3332120882121

= 6368552073445   - 3323032741011

= 3045519332434   + 3410486012111

= 6456005344545   - 2116052101111

= 4339953243434   - 1060421211110

= 3279532032324   - 1524212311121

= 1755319721203   + 6202282511232

= 7957602232435   - 2421620112122

= 5535982120313   - 224161123222

= 5311820997091   - 2207629027984

= 3104191969107   - 2143888338174

= 960303630933   - 363333339606

= 596970291327   - 433272782152

= 163697509175   + 533322598624

= 697020107799   - 327221170203

= 369798937596   - 332211642433

= 37587295163   + 42315744530

= 79903039693   - 20933363364

= 58969676329   - 31333113174

= 27636563155   + 51331132403

= 78967695558   - 11311340031

= 67656355527   - 11113200351

= 56543155176   - 11112404611

= 45430750565   - 11137255111

= 34293495454   - 12761541111

= 21531954343   - 14228411111

= 7303543232   - 4332111115

= 2971432117   + 7263111065

= 10234543182   + 12111112761

= 22345655943   - 1111104511

= 21234551432   - 11111043110

= 10123508322   + 11112585101

= 21236093423   - 11136961211

= 10099132212   + 10908210111

= 21007342323   - 11074121111

= 9933221212   - 601011117

= 9332210095   - 6010110944

= 3322099151   - 102908442

= 3219190709   - 1188897796

= 2030292913   + 2332777821

= 4363070734   - 1333777410

= 3029293324   + 3277760121

= 6307053445   - 3377521011

= 2929532434   + 7774212112

= 10703744546   + 17734301125

= 28438045671   + 64158411161

= 92596456832   - 73432112517

= 19164344315   + 88521101244

= 107685445559   + 171231010048

= 278916455607   + 511852101675

= 790768557282   - 297123025665

= 493645531617   + 563210225563

= 1056855757180   + 1512302226781

= 2569157983961   + 3138422156351

= 5707580140312   - 2772381343213

= 2935198797099   + 7624811227907

= 10560010025006   + 15160110235065

= 25720120260071   + 32521122460761

= 58241242720832   - 36231225528513

= 22010017192319   - 2110166871287

= 19899850321032   + 81101353111311

= 101001203432343   + 111011231111112

= 212012434543455   - 112112111111103

= 99900323432352   - 903111111237

= 98997212321115   - 11025111110044

= 87972101211071   - 12251111101767

= 75720990109304   - 22529091196343

= 53191898912961   - 22887111817354

= 30304787095607   + 33343117941674

= 63647905037281   - 33232955345675

= 30414949691606   + 34335553385663

= 64750503077269   - 23255533705433

= 41494969371836   - 33555336467532

= 7939632904304   - 2663317941343

= 5276314962961   - 3513235347354

= 1763079615607   + 6133723541676

= 7896803157283   - 1132832425654

= 6763970731629   - 1136277425473

= 5627693306156   - 1451360365411

= 4176332940745   - 3613017547311

= 563315393434   - 130242661111

= 433072732323   - 103755411111

= 329317321212   - 176264111111

= 153053210101   + 423521111110

= 576574321211   - 211231111104

= 365343210107   - 312111111174

= 53232098933   - 21112911602

= 32119187331   - 11088714022

= 21030473309   - 11334340397

= 9696132912   - 3335217817

= 6360915095   - 3369845941

= 2991069154   + 7081638412

= 10072707566   + 10755772105

= 20828479671   + 28664323161

= 49492802832   + 55576826512

= 105069629344   + 155633476103

= 260703105447   + 467732151035

= 728435256482   - 564123312465

= 164311944017   + 521208504166

= 685520448183   - 230324047753

= 455196400430   - 104832404134

= 350363996296   - 253336034733

= 97027961563   - 27252354136

= 69775607427   - 32021673251

= 37753934176   + 40226613613

= 77980547789   - 2185130112

= 75795417677   - 22241361100

= 53554056577   - 22014511202

= 31539545375   - 24264112422

= 7275432953   - 5521117424

= 1754315529   + 6211240378

= 7965555907   - 2310004970

= 5655550937   - 1100059642

= 4555491295   - 1001581741

= 3553909554   - 2026994011

= 1526915543   + 4343840112

= 5870755655   - 3177201100

= 2693554555   + 4362011003

= 7055565558   + 7500110031

= 14555675589   + 31001120318

= 45556795907   - 10011244973

= 35545550934   - 20110059611

= 15435491323   + 41121582112

= 56557073435   - 11027741120

= 45529332315   - 10376011241

= 35153321074   - 24420111731

= 10733209343   + 17401296112

= 28134505455   + 67211551103

= 95346056558   - 42126511031

= 53219545527   - 21184110352

= 32035435175   - 12321124622

= 19714310553   + 82631215022

= 102345525575   + 121110330224

= 223455855799   - 11103302207

= 212352553592   - 111233022470

= 101119531122   + 110084220101

= 211203751223   - 101234241011

= 109969510212   + 190334412111

= 300303922323   + 303336701110

= 603640623433   + 633246411103

= 1236887034536   - 1132017311235

= 104869723301   + 144232510310

= 249102233611   + 258120103501

= 507222337112   + 575001046013

= 1082223383125   + 1860010552134

= 2942233935259   + 7520106623347

= 10462340558606   + 14241145032665

= 24703485591271   - 23731430481561

= 972055109710   - 252504192619

= 719550917091   - 684059867986

= 35491049105   - 21581458152

= 13909590953   + 26994499422

= 40904090375   + 49944993421

= 90849083796   + 98459854233

= 189308938029   + 716381658278

= 905690596307   + 951395433372

= 1857086029679   + 7327826273128

= 9184912302807   - 8745811326872

= 439100975935   - 168109224621

= 270991751314   + 579086242232

= 850077993546   - 350702062122

= 499375931424   + 506424623220

= 1005800554644   + 1053805012203

= 2059605566847   + 2543650102435

= 4603255669282   - 2631301037662

= 1971954631620   + 8268412325421

= 10240366957041   + 12243303427430

= 22483670384471   - 2453173540361

= 20030496844110   + 20334532403012

= 40365029247122   + 43315277236102

= 83680306483224   - 53283362451024

= 30396944032200   + 33633504310203

= 64030448342403   - 24334045122433

= 39696403219970   + 63332431180273

= 103028834400243   + 133260510402212

= 236289344802455   - 134616104822103

= 101673239980352   + 115141160183231

= 216814400163583   - 152730401532351

= 64083998631232   - 24856012321114

= 39227986310118   + 67052123211075

= 106280109521193   + 164681194310862

= 270961303832055   + 579352335512503

= 850313639344558   - 353223366101030

= 497090273243528   + 527992541212364

= 1025082814455892   + 1235866730103171

= 2260949544559063   - 469554101049631

= 1791395443509432   + 6282641012595111

= 8074036456104543   + 8734332115141115

= 16808368571245658   + 52885323261211140

= 69693691832456790   - 33363387512111296

= 36330304320345496   - 33033341123111532

= 3296963197233964   - 1733332825106321

= 1563630372127643   + 4133333451151212

= 5696963823278855   - 1333335611510300

= 4363628211768555   - 1333466106123001

= 3030162105645554   + 3331541151210011

= 6361703256855565   - 3356731312300111

= 3004971944555454   + 3045268501001111

= 6050240445556565   + 6552244010011111

= 12602484455567676   + 14622440100111116

= 27224924555678790   + 55025721001111300

= 82250645556790080   - 60356210011290890

= 21894435545499190   - 17150120111508892

= 4744315433990300   - 3301241106093304

= 1443074327896996   + 3013731151133035

= 4456805479030031   - 112851329330323

= 4343954149699708   - 1116413353302784

= 3227540796396924   - 1052147233633721

= 2175393562763203   - 1622662145131231

= 552731417631972   - 35423361328253

= 517308056303719   - 464388513334684

= 52919542969035   - 37884127339320

= 15035415629715   + 45321341472644

= 60356757102359   + 63211226121243

= 123567983223602   - 112112151013621

= 11455832209981   - 3103510290170

= 8352321919811   - 5231118881707

= 3121203038104   - 2111233357141

= 1009969680963   + 1090333289332

= 2100302970295   - 1103327272743

= 996975697552   - 33221322037

= 963754375515   - 334211420444

= 629542955071   - 474127405765

= 155415549306   + 401340156365

= 556755705671   - 11202751164

= 545552954507   - 110037411572

= 435515542935   - 120440127621

= 315075415314   - 245721342231

= 69354073083   - 36214743853

= 33139329230   - 2266177133

= 30873152097   + 38142432924

= 69015585021   - 39140335215

= 29875249806   + 71123251864

= 100998501670   + 109013515171

= 210012016841   - 110112152431

= 99899864410   - 1101220319

= 98798644091   - 11212204988

= 87586439103   - 12322168135

= 75264270968   - 23422579321

= 51841691647   - 47435385232

= 4406306415   - 463362341

= 3942944074   + 6527504731

= 10470448805   + 14374040854

= 24844489659   - 24400413147

= 444076512   - 4711412

= 439365100   - 166314104

= 273050996   + 543559034

= 816610030   - 750510338

= 66099692   - 6903374

= 59196318   - 48833273

= 10363045   + 13333414

= 23696459   - 13332147

= 10364312   + 13321211

= 23685523   - 13230311

= 10455212   + 14103111

= 24558323   - 21035111

= 3523212   - 2311111

= 1212101   - 1111110

= 100991   + 109080

= 210071   - 110761

= 99310   - 6219

= 93091   - 63988

= 29103   + 78131

= 107234   + 175113

= 282347   + 661135

= 943482   - 511467

= 432015   - 112141

= 319874   - 281131

= 38743   + 51310

= 90053   + 90526

= 180579   + 785228

= 965807   - 313872

= 651935   - 148621

= 503314   + 530231

= 1033545   + 1302114

= 2335659   - 1021147

= 1314512   + 2231411

= 3545923   - 2114710

= 1431213   + 3121122

= 4552335   - 1031021

= 3521314   - 2312231

= 1209083   + 1299852

= 2508935   + 3581623

= 6090558   + 6995032

= 13085590   + 23830491

= 36916081   - 33856872

= 3059209   + 3547296

= 6606505   - 661551

= 5944954   - 4505411

= 1439543   + 3164112

= 4603655   - 2633101

= 1970554   + 8275013

= 10245567   + 12210116

= 22455683   - 2101251

= 20354432   + 23210110

= 43564542   - 12121122

= 31443420   - 23011223

= 8432197   - 4111821

= 4320376   - 1123412

= 3196964   - 2833321

= 363643   - 333210

= 30433   + 34100

= 64533   - 21203

= 43330   - 10034

= 33296   - 1733

= 31563   - 24130

= 7433   - 3104

= 4329   - 1175

= 3154   - 2411

= 743   - 314

= 429   - 275

= 154   + 413

= 567   - 112

= 455   - 101

= 354   - 211

= 143   + 312

= 455   LOOP!

__________

Many thanks to all contributors!

Best,

É.