Hello Math-Fun & SeqFan,

WARNING!

This sequence is *not* for OEIS mathematicians!

- it is base-dependent!

- it has black spots on its shirt!

- it is badly defined (in pidgin-English)!

- it is computed by hand...

(I would recommend it only for drunken ophthalmologists.)

... Now proceed to 1-click reading © at your own risks!

-------------------------------------------------------

1,12,35,94,135,186,248,331,344,387,461,475,530,535,590,595,651,667,744,791,809,908,997,1068,1149,1240,1241,1252,...

The difference between a(n) and a(n-1) is always a 2-digit figure -- which is reproduced to the left and right of the separating comma:

Sequence: 1, 12, 35, 94, 135, 186, 248, 331, 344, 387, 461, 475, 530, 535, ...

Differences:  11  23  59  41   51   62   83   13   43   74   14   55   05   ...

You will agree that “05” is not the common way to represent a difference of five units (in yellow)... Well, so it is here!

Could someone check if the sequence grows infinitely?

[If you start the sequence with 3 instead of 1 you’ll get blocked very quickly: 3,36 -- END.]

[Self-blocking integers are: 18,27,36,45,54,63,72 and 81]

I could trace only four chains leading to such dead-ends:

3,36 END

31,45 END

15,72 END

43,81 END.

---------------------------------------------------------

I’ve examined too a few sequences showing the |absolute difference| between a(n) and a(n-1).

I had thus more choices for a(n+1). So I decided to build a sequence with differences < 100 and differences > 9 (in order to avoid leading zeros). I wanted also the sequence to be kept as low as possible -- and not self-blocking -- and not self-looping either...

Well, I’m not sure all those criteria are compatible between them and define properly sequences like this one:

1,12,35,94,135,78,159,251,239,148,62,91,74,115,166,105,156,88,4,48,129,221,209,118,199...

Anyway, this was great fun to investigate!

Best,

É.

---------------------------------------------------------

The above message was posted by me on rec.puzzles as well. I got this answer from “The Qurqirish Dragon” almost immediately:

I noticed one problem with the rule:

Take the sequence starting with 2:

2, (+22) 24, (+47) 71, ?

Is the next value 89 or 90? Both follow the given rule:

2, (+22) 24, (+47) 71, (+18) 89, (+91) 180, ...

2, (+22) 24, (+47) 71, (+19) 90, (+09) 99, (+91) 190, ...

This problem will happen whenever a given addition works resulting in a number consisting of all 9s (except for the first digit, which must be less than 9).

I got then the same remark from Nicolas Graner, a friend of mine I had written too:

Que fais-tu si tu rencontres 14, 33, 52 ou 71 qui ont deux successeurs

possibles ?

[What do you do with 14, 33, 52 or 71 which have two possible successors?]

To both I wrote:

Well done! I overlooked that possibility -- please keep the sequence as low as possible!

Then I got this from Zak Seidov -- another friend:

For checking purposes I give first and 10th hundreds terms of seq:

1,12,35,94,135,186,248,331,344,387,461,475,530,535,590,595,651,667,744,791,809,908,997,

1068,1149,1240,1241,1252,1273,1304,1345,1396,1457,1528,1609,1700,1701,1712,1733,1764,

1805,1856,1917,1988,2070,2072,2094,2136,2198,2280,2282,2304,2346,2408,2490,2492,2514,

2556,2618,2700,2702,2724,2766,2828,2910,2912,2934,2976,3039,3132,3155,3208,3291,3304,

3347,3420,3423,3456,3519,3612,3635,3688,3771,3784,3827,3900,3903,3936,3999,4093,4127,

4201,4215,4269,4363,4397,4471,4485,4539,4633,

<...>

44303,44337,44411,44425,44479,44573,44607,44681,44695,44749,44843,44877,44951,44965,

45019,45113,45147,45221,45235,45289,45383,45417,45491,45505,45559,45653,45687,45761,

45775,45829,45923,45957,46031,46045,46099,46193,46227,46301,46315,46369,46463,46497,

46571,46585,46639,46733,46767,46841,46855,46909,47003,47037,47111,47125,47179,47273,

47307,47381,47395,47449,47543,47577,47651,47665,47719,47813,47847,47921,47935,47989,

48083,48117,48191,48205,48259,48353,48387,48461,48475,48529,48623,48657,48731,48745,

48799,48893,48927,49001,49015,49069,49163,49197,49271,49285,49339,49433,49467,49541,

49555,49609,

Zak

Then I got this, from Edwin Clark:

Eric,

If I didn't make a mistake in my Maple program:

The last term in your sequence --call it a(n) is

a(2137453)=99999945;

---but there is no next term.

Best wishes,

Edwin

Waow! How quick, Edwin!

Zak answered him (on SeqFan):

Edwin,

This dirty code

a=49703;c=1001;Do[ida=a+10Mod[a,10];Do[b=ida+i;If[i==IntegerDigits[b][[1]],a=b;c++;Break[],If[i&#62513;9,Print[a];Goto[en]]],{i,0,9}],{10000000}];Label[en];Print[{c,a,b,"end!"}]

99999945

{2137453,99999945,100000004,end!}

confirms your great result!

Ed Murphy sent to rec.puzzles a message about “blocked sequences”:

a(1) is chosen arbitrarily.

a(n+1) can be any number satisfying the following conditions:

1) d = a(n+1)-a(n) < 100

2) a(n) mod 10 = floor(d/10)

3) d mod 10 = floor(a(n+1)/10^floor(log10(a(n+1))))

In other words, the difference between a(n) and a(n+1) is a two-digit number that starts with the same digit as the last digit of a(n) (or is < 10 if a(n) ends in 0), and ends with the same digit as the first digit of a(n+1).

A given number may have 0, 1, or >1 candidate successors.

Sample chain:

1, 12, 35, 94, 135, 186, 248, 331, 344, 387, 461, 475, 530, 535, 590

11  23  59  41   51   62   83   13   43   74   14   55    5   55

Sample chains that become blocked:

3, 36

31, 45

15, 72

43, 81

Which choices for a(1) result in a block?  Here's a first stab:

10  for s = 1 to 100

20    dim c[100]; c[1] = s, cc = 1

30    for i = 1 to 100000

40      dim nc[100]; np = 0

50      for ci = 1 to cc

60        for d = mod(c[ci],10)*10+1 to mod(c[ci],10)*10+9

70          d\$ = str(d), n\$ = str(c[ci]+d)

80          if mid(d\$,-1,1) = mid(n\$,1,1) then np += 1, nc[np] = c[ci]+d

90        next d

100     next ci

110     if np = 0 then print s, " blocks on iteration ", i; break

120   c{all} = nc{all}, cc = np

130   next i

140 next s

3 blocks on iteration  2

7 blocks on iteration  15

15 blocks on iteration  2

18 blocks on iteration  1

19 blocks on iteration  21482

21 blocks on iteration  2074

25 blocks on iteration  193

27 blocks on iteration  1

28 blocks on iteration  197

31 blocks on iteration  2

34 blocks on iteration  2073

36 blocks on iteration  1

37 blocks on iteration  196

39 blocks on iteration  20

41 blocks on iteration  19

42 blocks on iteration  1981

43 blocks on iteration  2

45 blocks on iteration  1

49 blocks on iteration  193

53 blocks on iteration  21

54 blocks on iteration  1

56 blocks on iteration  18

60 blocks on iteration  204

63 blocks on iteration  1

65 blocks on iteration  2100

66 blocks on iteration  203

68 blocks on iteration  1980

72 blocks on iteration  1

74 blocks on iteration  20

75 blocks on iteration  2136

81 blocks on iteration  1

82 blocks on iteration  2072

83 blocks on iteration  192

85 blocks on iteration  14

86 blocks on iteration  1983

90 blocks on iteration  21

92 blocks on iteration  20

98 blocks on iteration  205

99 blocks on iteration  20

Alas, Qurqirish Dragon is wrong; reaching a three-digit sum does not guarantee that the sequence can be extended indefinitely.

Example:

7, 85, 136, 197, 269, 362, 385, 439, 534, 579, 675, 732, 759, 857, 936

Notice how the number of iterations before a block clump around 2, 20, 200, 2000, 20000.  Look at that sequence starting with 7:  From 136 to 936, the differences increase roughly linearly within the 11-99 range, averaging somewhere around 50; the amount of increase is approximately 1000, so the number of increases is approximately 1000/50 = 20.  The sequences that block after approximately 200 iterations are probably hitting similar tar pits at 9xxx -> 1xxxx, and so forth.

ObPuzzle:  What is the largest number of choices we can have at any iteration?  IOW, how large do the C and NC arrays need to be to guarantee they won't overflow? Adding the following lines:

125   if m < np then m = np

150 print m

indicates that the maximum number this program actually encounters within 100 iterations is 4, within 1,000 is 5, and within 100,000 is 6.

What if d = abs(a(n+1)+a(n)), i.e. the sequence is not necessarily monotonically increasing?  Which choices for a(1) result in a block? Which choices result in a loop?

Sample sequence:

1, 12, 35, 94, 135, 78, 159, 251, 239, 148, 62, 91, 74, 115, 166,

105, 156, 88, 4, 48, 129, 221, 209, 118, 199

What if d must be > 10?  Adding the following line:

55        if mod(c[ci],10) = 0 then continue

indicates that only a few numbers survive to the 20-iteration hump, and none of them get very far past it:

18 -> 5, 11, 17, 23, 25, 38, 55, 58, 61, 65, 75, 76, 78, 83, 86, 96

19 -> 5, 11, 17, 23, 25, 38, 55, 58, 61, 65, 75,     78,         96

20 -> 5, 11, 17, 23,             58, 61,             78,         96

21 -> 5, 11, 17, 23,                 61,                         96

22 -> 5, 11, 17

23 -> nothing

What about bases other than 10?

Indeed, Ed!

End of the story -- Zak and Neil have turned this into an OEIS sequence: A121805

Thanks to all contributors,

É.

---------------------------------------------------------

A year later (dec. 12th, 2007) David Wilson posted this on Seq-Fans:

Every positive integer n has at most one comma sequence predecessor p(n),

that is, a number which may precede it in a comma sequence. p(n) is

defined for all positive integers except for the 50 integers in the

following set

S = {

1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

13, 14, 15, 16, 17, 18, 19, 20, 21, 25,

26, 27, 28, 29, 30, 31, 32, 37, 38, 39,

40, 41, 42, 43, 49, 50, 51, 52, 53, 54,

62, 63, 64, 65, 74, 75, 76, 86, 87, 98

}

p(n) is undefined for n in S, for all other n in N, p(n) < n.

Starting with any positive integer n, we can iterate p on n until we

reach a unique element a(n) in S, called the ancestor of n.

Going forward, most positive integers n have a unique successor n.

However, there are a smattering of integers that have no successor,

specifically, the integers in the set

T = { (10^x + 9y) - 100 : x >= 2 and 2 <= y <= 9 }

That is

T = {

18, 27, 36, 45, 54, 63, 72, 81,

918, 927, 936, 945, 954, 963, 972, 981,

9918, 9927, 9936, 9945, 9954, 9963, 9972, 9981,

...

}

If a comma sequence reaches an element of T, the sequence ends there.

There is also a sparse set of integers that have two successors, these

form the strangely similar set

B = { (10^x + 9)y - 100 ; x >= 2 and 2 <= y <= 9 }

or

B = {

118, 227, 336, 445, 554, 663, 772, 881,

1918, 2927, 3936, 4945, 5954, 6963, 7972, 8981,

19918, 29927, 39936, 49945, 59954, 69963, 79972, 89981,

...

}

(10^x + 9)y - 100 has the two successors (10^x)y - 1 and (10^x)y. No

positive integer has more than two successors.

If a comma sequence reaches an element of B, it is possible to continue

the sequence in two ways from that element.

You will notice that comma sequence terminating and branching elements

all occur just before (within 100 of) an initial digit change. On intervals

where the initial digit of its elements remains constant, however, a comma

sequence behaves very nicely, with periodic first differences. This allows

one to do some modular magic to skip over these intervals in constant time,

which allows us to quickly compute a(n) for very large n.

Using this knowledge, I wrote a program to compute m(n), the largest

possible element in a comma sequence starting with n, for n in S.  It turns

out that there are infinite comma sequences starting with 20, a comma

sequence with any other start value in S terminates at or before 10^365-82.

n    m(n)

1    10^25-28

2    10^16-82

3    10^2-64

4    10^7-55

5    10^16-64

6    10^42-64

7    10^3-64

8    10^13-28

9    10^24-19

10    10^13-19

13    10^87-37

14    10^11-82

15    10^2-28

16    10^14-55

17    10^54-55

18    10^2-82

19    10^6-19

20    Infinity

21    10^5-19

25    10^4-37

26    10^7-28

27    10^2-73

28    10^4-73

29    10^8-64

30    10^365-82

31    10^2-55

32    10^9-82

37    10^4-82

38    10^17-37

39    10^3-82

40    10^30-82

41    10^3-46

42    10^5-73

43    10^2-19

49    10^4-55

50    10^18-73

51    10^18-55

52    10^21-19

53    10^3-28

54    10^2-46

62    10^7-19

63    10^2-37

64    10^132-19

65    10^5-37

74    10^3-55

75    10^5-46

76    10^24-46

86    10^5-82

87    10^12-82

98    10^4-64

Great results -- thanks, David, for the 20-infinite comma sequence!

---------------------------------------

1001 terms computed by Zak Seidov.

[the difference between terms n and (n+1) is “uv”, u being the last digit of n and v the first digit of n+1).

Example: for n=28 and (n+1)=29 we have 1252-1273=21]

# Zak Seidov, Dec 11, 2006

1   1

2   12

3   35

4   94

5   135

6   186

7   248

8   331

9   344

10   387

11   461

12   475

13   530

14   535

15   590

16   595

17   651

18   667

19   744

20   791

21   809

22   908

23   997

24   1068

25   1149

26   1240

27   1241

28   1252

29   1273

30   1304

31   1345

32   1396

33   1457

34   1528

35   1609

36   1700

37   1701

38   1712

39   1733

40   1764

41   1805

42   1856

43   1917

44   1988

45   2070

46   2072

47   2094

48   2136

49   2198

50   2280

51   2282

52   2304

53   2346

54   2408

55   2490

56   2492

57   2514

58   2556

59   2618

60   2700

61   2702

62   2724

63   2766

64   2828

65   2910

66   2912

67   2934

68   2976

69   3039

70   3132

71   3155

72   3208

73   3291

74   3304

75   3347

76   3420

77   3423

78   3456

79   3519

80   3612

81   3635

82   3688

83   3771

84   3784

85   3827

86   3900

87   3903

88   3936

89   3999

90   4093

91   4127

92   4201

93   4215

94   4269

95   4363

96   4397

97   4471

98   4485

99   4539

100   4633

101   4667

102   4741

103   4755

104   4809

105   4903

106   4937

107   5012

108   5037

109   5112

110   5137

111   5212

112   5237

113   5312

114   5337

115   5412

116   5437

117   5512

118   5537

119   5612

120   5637

121   5712

122   5737

123   5812

124   5837

125   5912

126   5937

127   6013

128   6049

129   6145

130   6201

131   6217

132   6293

133   6329

134   6425

135   6481

136   6497

137   6573

138   6609

139   6705

140   6761

141   6777

142   6853

143   6889

144   6985

145   7042

146   7069

147   7166

148   7233

149   7270

150   7277

151   7354

152   7401

153   7418

154   7505

155   7562

156   7589

157   7686

158   7753

159   7790

160   7797

161   7874

162   7921

163   7938

164   8026

165   8094

166   8142

167   8170

168   8178

169   8266

170   8334

171   8382

172   8410

173   8418

174   8506

175   8574

176   8622

177   8650

178   8658

179   8746

180   8814

181   8862

182   8890

183   8898

184   8986

185   9055

186   9114

187   9163

188   9202

189   9231

190   9250

191   9259

192   9358

193   9447

194   9526

195   9595

196   9654

197   9703

198   9742

199   9771

200   9790

201   9799

202   9898

203   8883

204   10058

205   10139

206   10230

207   10231

208   10242

209   10263

210   10294

211   10335

212   10386

213   10447

214   10518

215   10599

216   10690

217   10691

218   10702

219   10723

220   10754

221   10795

222   10846

223   10907

224   10978

225   11059

226   11150

227   11151

228   11162

229   11183

230   11214

231   11255

232   11306

233   11367

234   11438

235   11519

236   11610

237   11611

238   11622

239   11643

240   11674

241   11715

242   11766

243   11827

244   11898

245   11979

246   12070

247   12071

248   12082

249   12103

250   12134

251   12175

252   12226

253   12287

254   12358

255   12439

256   12530

257   12531

258   12542

259   12563

260   12594

261   12635

262   12686

263   12747

264   12818

265   12899

266   12990

267   12991

268   13002

269   13023

270   13054

271   13095

272   13146

273   13207

274   13278

275   13359

276   13450

277   13451

278   13462

279   13483

280   13514

281   13555

282   13606

283   13667

284   13738

285   13819

286   13910

287   13911

288   13922

289   13943

290   13974

291   14015

292   14066

293   14127

294   14198

295   14279

296   14370

297   14371

298   14382

299   14403

300   14434

301   14475

302   14526

303   14587

304   14658

305   14739

306   14830

307   14831

308   14842

309   14863

310   14894

311   14935

312   14986

313   15047

314   15118

315   15199

316   15290

317   15291

318   15302

319   15323

320   15354

321   15395

322   15446

323   15507

324   15578

325   15659

326   15750

327   15751

328   15762

329   15783

330   15814

331   15855

332   15906

333   15967

334   16038

335   16119

336   16210

337   16211

338   16222

339   16243

340   16274

341   16315

342   16366

343   16427

344   16498

345   16579

346   16670

347   16671

348   16682

349   16703

350   16734

351   16775

352   16826

353   16887

354   16958

355   17039

356   17130

357   17131

358   17142

359   17163

360   17194

361   17235

362   17286

363   17347

364   17418

365   17499

366   17590

367   17591

368   17602

369   17623

370   17654

371   17695

372   17746

373   17807

374   17878

375   17959

376   18050

377   18051

378   18062

379   18083

380   18114

381   18155

382   18206

383   18267

384   18338

385   18419

386   18510

387   18511

388   18522

389   18543

390   18574

391   18615

392   18666

393   18727

394   18798

395   18879

396   18970

397   18971

398   18982

399   19003

400   19034

401   19075

402   19126

403   19187

404   19258

405   19339

406   19430

407   19431

408   19442

409   19463

410   19494

411   19535

412   19586

413   19647

414   19718

415   19799

416   19890

417   19891

418   19902

419   19923

420   19954

421   19995

422   20047

423   20119

424   20211

425   20223

426   20255

427   20307

428   20379

429   20471

430   20483

431   20515

432   20567

433   20639

434   20731

435   20743

436   20775

437   20827

438   20899

439   20991

440   21003

441   21035

442   21087

443   21159

444   21251

445   21263

446   21295

447   21347

448   21419

449   21511

450   21523

451   21555

452   21607

453   21679

454   21771

455   21783

456   21815

457   21867

458   21939

459   22031

460   22043

461   22075

462   22127

463   22199

464   22291

465   22303

466   22335

467   22387

468   22459

469   22551

470   22563

471   22595

472   22647

473   22719

474   22811

475   22823

476   22855

477   22907

478   22979

479   23071

480   23083

481   23115

482   23167

483   23239

484   23331

485   23343

486   23375

487   23427

488   23499

489   23591

490   23603

491   23635

492   23687

493   23759

494   23851

495   23863

496   23895

497   23947

498   24019

499   24111

500   24123

501   24155

502   24207

503   24279

504   24371

505   24383

506   24415

507   24467

508   24539

509   24631

510   24643

511   24675

512   24727

513   24799

514   24891

515   24903

516   24935

517   24987

518   25059

519   25151

520   25163

521   25195

522   25247

523   25319

524   25411

525   25423

526   25455

527   25507

528   25579

529   25671

530   25683

531   25715

532   18032

533   25839

534   25931

535   25943

536   25975

537   26027

538   26099

539   26191

540   26203

541   26235

542   26287

543   26359

544   26451

545   26463

546   26495

547   26547

548   26619

549   26711

550   26723

551   26755

552   26807

553   26879

554   26971

555   26983

556   27015

557   27067

558   27139

559   27231

560   27243

561   27275

562   27327

563   27399

564   27491

565   27503

566   27535

567   27587

568   27659

569   27751

570   27763

571   27795

572   27847

573   27919

574   28011

575   28023

576   28055

577   28107

578   28179

579   28271

580   28283

581   28315

582   28367

583   28439

584   28531

585   28543

586   28575

587   28627

588   28699

589   28791

590   28803

591   28835

592   28887

593   28959

594   29051

595   29063

596   29095

597   29147

598   29219

599   29311

600   29323

601   29355

602   29407

603   29479

604   29571

605   29583

606   29615

607   29667

608   29739

609   29831

610   29843

611   29875

612   29927

613   29999

614   30092

615   30115

616   30168

617   30251

618   30264

619   30307

620   30380

621   30383

622   30416

623   30479

624   30572

625   30595

626   30648

627   30731

628   30744

629   30787

630   30860

631   30863

632   30896

633   30959

634   31052

635   31075

636   31128

637   31211

638   31224

639   31267

640   31340

641   31343

642   31376

643   31439

644   31532

645   31555

646   31608

647   31691

648   31704

649   31747

650   31820

651   31823

652   31856

653   31919

654   32012

655   32035

656   32088

657   32171

658   32184

659   32227

660   32300

661   32303

662   32336

663   32399

664   32492

665   32515

666   32568

667   32651

668   32664

669   32707

670   32780

671   32783

672   32816

673   32879

674   32972

675   32995

676   33048

677   33131

678   33144

679   33187

680   33260

681   33263

682   33296

683   33359

684   33452

685   33475

686   33528

687   33611

688   33624

689   33667

690   33740

691   33743

692   33776

693   33839

694   33932

695   33955

696   34008

697   3094

698   34104

699   34147

700   34220

701   34223

702   34256

703   34319

704   34412

705   34435

706   34488

707   34571

708   34584

709   34627

710   34700

711   34703

712   34736

713   34799

714   34892

715   34915

716   34968

717   35051

718   35064

719   35107

720   35180

721   35183

722   35216

723   35279

724   35372

725   35395

726   35448

727   35531

728   35544

729   35587

730   35660

731   35663

732   35696

733   35759

734   35852

735   35875

736   35928

737   36011

738   36024

739   36067

740   36140

741   36143

742   36176

743   36239

744   36332

745   36355

746   36408

747   36491

748   36504

749   36547

750   36620

751   36623

752   36656

753   36719

754   36812

755   36835

756   36888

757   36971

758   36984

759   37027

760   37100

761   37103

762   37136

763   37199

764   37292

765   37315

766   37368

767   37451

768   37464

769   37507

770   37580

771   37583

772   37616

773   37679

774   37772

775   37795

776   37848

777   37931

778   37944

779   37987

780   38060

781   38063

782   38096

783   38159

784   38252

785   38275

786   38328

787   38411

788   38424

789   38467

790   38540

791   38543

792   38576

793   38639

794   38732

795   38755

796   38808

797   38891

798   38904

799   38947

800   39020

801   39023

802   39056

803   39119

804   39212

805   39235

806   39288

807   39371

808   39384

809   39427

810   39500

811   39503

812   39536

813   39599

814   39692

815   39715

816   39768

817   39851

818   39864

819   39907

820   39980

821   39983

822   40017

823   40091

824   40105

825   40159

826   40253

827   40287

828   40361

829   40375

830   40429

831   40523

832   40557

833   40631

834   40645

835   40699

836   40793

837   40827

838   40901

839   40915

840   40969

841   41063

842   41097

843   41171

844   41185

845   41239

846   41333

847   41367

848   41441

849   41455

850   41509

851   41603

852   41637

853   41711

854   41725

855   41779

856   41873

857   41907

858   41981

859   41995

860   42049

861   42143

862   42177

863   42251

864   42265

865   42319

866   42413

867   42447

868   42521

869   42535

870   42589

871   42683

872   42717

873   42791

874   42805

875   42859

876   42953

877   42987

878   43061

879   43075

880   43129

881   43223

882   43257

883   43331

884   43345

885   43399

886   43493

887   43527

888   43601

889   43615

890   43669

891   43763

892   43797

893   43871

894   43885

895   43939

896   44033

897   44067

898   44141

899   44155

900   44209

901   44303

902   44337

903   44411

904   44425

905   44479

906   44573

907   44607

908   44681

909   44695

910   44749

911   44843

912   44877

913   44951

914   44965

915   45019

916   45113

917   45147

918   45221

919   45235

920   45289

921   45383

922   45417

923   45491

924   45505

925   45559

926   45653

927   45687

928   45761

929   45775

930   45829

931   45923

932   45957

933   46031

934   46045

935   46099

936   46193

937   46227

938   46301

939   46315

940   46369

941   46463

942   46497

943   46571

944   46585

945   46639

946   46733

947   46767

948   46841

949   46855

950   46909

951   47003

952   47037

953   47111

954   47125

955   47179

956   47273

957   47307

958   47381

959   47395

960   47449

961   47543

962   47577

963   47651

964   47665

965   47719

966   47813

967   47847

968   47921

969   47935

970   47989

971   48083

972   48117

973   48191

974   48205

975   48259

976   48353

977   48387

978   48461

979   48475

980   48529

981   48623

982   48657

983   48731

984   48745

985   48799

986   48893

987   48927

988   49001

989   49015

990   49069

991   49163

992   49197

993   49271

994   49285

995   49339

996   49433

997   49467

998   49541

999   49555

1000   49609

1001   49703

...

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