Add or subtract the result.
Iterate.
Hello Math-Fun,
Here is another
stupid iteration – which leads nowhere, probably.
Start with (my date
of birth) for instance: 1951
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:
http://chesswanks.com/num/asi/199.txt
I have added
an asterisk (*) beside the maximum number to make it easier to find.
[Eric]:
Hello Hans, I don’t understand your [link]
[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 10645443531 26856743532 69168243533 30641843534 66879343535 64753043536 41529443537 7154443538 744143539 440543540 395443541 1036543542 2367943543 1055243544 2558343545 5593443546 5132343547 921143548 210343549 97243550 71543551 7343552 2943553 10643554 27143555 83243556 31643557 6343558 3043559 63
The maximum “altitude” of 10886
was:
18602 47268036226040834444456790454609106572346054596959 0848791030672352568049279004470723605455696919256962805044566787970784675907
... 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 19767599 102367600 223567601 211267602 110267603 98167604 80367605 163867606 699567607 395467608 1036567609 2367967610 1055267611 2558367612 5593467613 5132367614 921167615 210367616 97267617 71567618 7367619 2967620 10667621 27167622 83267623 31667624 6367625 3067626 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 0247065084892680879679262826963693455680469424030672844496369007
... 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 Nastos’ script,
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.