{{2,5},{3,11},{4,2},{5,39},{6,7},{7,10},{8,5},{9,13},{10,18},{11,27},{12,1},{13,265},{14,145},{15,108},{16,102},{17,102},{18,5},{19,79},{20,69},{21,37},{22,87},{23,12},{24,18},{25,148},{26,152},{27,206},{28,51},{29,56},{30,27},{31,308},{32,89},{33,95},{3

a(N) = k if the first occurrence of the digits of N is at the k-th place in N^(1/N)

Example 18^(1/18) = 1.174187253... and 18 appears beginning at the fifth place -> a(18)=5

J-M. Falcoz, April 2009

The terms, up to 10000 :

2,5

3,11

4,2

5,39

6,7

7,10

8,5

9,13

10,18

11,27

12,1

13,265

14,145

15,108

16,102

17,102

18,5

19,79

20,69

21,37

22,87

23,12

24,18

25,148

26,152

27,206

28,51

29,56

30,27

31,308

32,89

33,95

34,181

35,178

36,62

37,114

38,245

39,281

40,38

41,111

42,39

43,286

44,102

45,125

46,224

47,244

48,26

49,87

50,117

51,67

52,78

53,147

54,284

55,4

56,61

57,21

58,83

59,28

60,147

61,83

62,141

63,44

64,478

65,10

66,22

67,6

68,106

69,152

70,726

71,51

72,100

73,139

74,57

75,145

76,238

77,327

78,44

79,267

80,220

81,178

82,141

83,29

84,123

85,76

86,109

87,31

88,9

89,50

90,124

91,75

92,47

93,17

94,217

95,400

96,54

97,36

98,88

99,99

100,2900

101,269

102,894

103,1066

104,1

105,20

106,1489

107,46

108,1401

109,2400

110,346

111,2367

112,151

113,63

114,503

115,371

116,1831

117,1620

118,2252

119,522

120,961

121,1265

122,267

123,1054

124,16

125,328

126,514

127,76

128,3100

129,982

130,819

131,550

132,551

133,1135

134,372

135,17

136,2897

137,95

138,680

139,49

140,149

141,4582

142,71

143,671

144,73

145,3452

146,823

147,279

148,1375

149,1769

150,636

151,2002

152,2740

153,347

154,1344

155,1213

156,517

157,508

158,1089

159,659

160,573

161,4382

162,400

163,1682

164,1124

165,76

166,1819

167,437

168,475

169,1231

170,493

171,296

172,702

173,2899

174,382

175,1280

176,293

177,780

178,571

179,2509

180,1793

181,1624

182,714

183,657

184,125

185,3620

186,53

187,559

188,595

189,400

190,349

191,3139

192,2141

193,812

194,549

195,1712

196,686

197,684

198,64

199,408

200,1914

201,1434

202,228

203,883

204,403

205,2570

206,338

207,1256

208,2900

209,1077

210,110

211,277

212,474

213,31

214,1559

215,1439

216,125

217,858

218,12

219,234

220,1489

221,502

222,1097

223,851

224,2603

225,587

226,611

227,1116

228,669

229,589

230,877

231,849

232,535

233,39

234,1043

235,3

236,77

237,780

238,555

239,919

240,92

241,1085

242,87

243,215

244,557

245,1137

246,972

247,1024

248,4

249,1028

250,1897

251,678

252,1260

253,3125

254,455

255,521

256,97

257,672

258,419

259,1193

260,2244

261,1903

262,367

263,2051

264,810

265,1739

266,587

267,587

268,955

269,122

270,163

271,12

272,2631

273,1824

274,68

275,1087

276,74

277,1403

278,1970

279,1307

280,1582

281,1924

282,1351

283,998

284,450

285,804

286,503

287,135

288,335

289,1428

290,803

291,2661

292,1088

293,11

294,410

295,305

296,895

297,357

298,1760

299,5683

300,716

301,257

302,988

303,1058

304,692

305,356

306,174

307,27

308,1339

309,214

310,1527

311,216

312,450

313,189

314,124

315,1812

316,359

317,1662

318,359

319,4823

320,344

321,370

322,1077

323,30

324,3132

325,246

326,1642

327,1271

328,348

329,7

330,561

331,1246

332,794

333,1041

334,488

335,386

336,280

337,489

338,2827

339,982

340,944

341,442

342,765

343,2260

344,102

345,1165

346,91

347,545

348,1180

349,1241

350,473

351,2454

352,518

353,1994

354,72

355,957

356,384

357,1257

358,176

359,1141

360,1240

361,701

362,1534

363,2840

364,46

365,1120

366,1112

367,907

368,158

369,687

370,3382

371,443

372,189

373,1086

374,1032

375,718

376,1267

377,62

378,305

379,482

380,1297

381,630

382,1170

383,588

384,326

385,432

386,2770

387,1476

388,1087

389,190

390,938

391,47

392,1935

393,433

394,2137

395,713

396,720

397,1132

398,3073

399,535

400,914

401,760

402,3057

403,91

404,622

405,44

406,1801

407,690

408,596

409,25

410,1014

411,248

412,1794

413,376

414,211

415,404

416,1480

417,361

418,1933

419,1579

420,1471

421,1464

422,556

423,478

424,114

425,1578

426,870

427,1865

428,893

429,26

430,1243

431,90

432,1345

433,215

434,111

435,299

436,253

437,1303

438,603

439,289

440,262

441,65

442,339

443,1086

444,134

445,379

446,1823

447,569

448,965

449,106

450,631

451,1929

452,2578

453,941

454,38

455,50

456,86

457,962

458,20

459,2130

460,402

461,428

462,1721

463,2034

464,2929

465,2095

466,597

467,914

468,1748

469,884

470,768

471,285

472,29

473,831

474,1312

475,113

476,15

477,1977

478,968

479,457

480,87

481,1212

482,407

483,243

484,117

485,254

486,859

487,1206

488,354

489,1677

490,1186

491,452

492,4403

493,427

494,1304

495,1705

496,377

497,549

498,1707

499,49

500,736

501,301

502,1356

503,1123

504,1032

505,292

506,107

507,333

508,1144

509,3092

510,1501

511,690

512,679

513,1431

514,128

515,2163

516,1239

517,1255

518,2148

519,817

520,734

521,1333

522,36

523,1114

524,886

525,140

526,777

527,217

528,758

529,588

530,1500

531,4207

532,2234

533,1735

534,1070

535,390

536,760

537,1467

538,414

539,945

540,901

541,735

542,130

543,69

544,1068

545,199

546,1384

547,753

548,524

549,449

550,1812

551,517

552,2050

553,514

554,1524

555,554

556,1453

557,962

558,1037

559,154

560,554

561,114

562,448

563,1315

564,226

565,29

566,197

567,2604

568,1054

569,298

570,208

571,2045

572,10

573,1124

574,602

575,870

576,360

577,769

578,1380

579,101

580,1732

581,214

582,436

583,1606

584,714

585,1094

586,1888

587,111

588,116

589,133

590,1023

591,81

592,1521

593,344

594,674

595,187

596,5159

597,2089

598,541

599,1154

600,330

601,4035

602,1346

603,436

604,281

605,1890

606,554

607,402

608,1068

609,3351

610,1779

611,780

612,2011

613,1768

614,973

615,1564

616,118

617,3870

618,15

619,1211

620,814

621,307

622,560

623,1002

624,385

625,748

626,975

627,40

628,404

629,271

630,741

631,1658

632,691

633,224

634,718

635,292

636,307

637,703

638,706

639,91

640,2709

641,1640

642,975

643,547

644,1186

645,4041

646,1427

647,375

648,732

649,864

650,2211

651,1089

652,562

653,653

654,110

655,722

656,906

657,443

658,285

659,1173

660,21

661,3144

662,1521

663,532

664,862

665,924

666,1465

667,1600

668,158

669,650

670,73

671,17

672,1553

673,109

674,3808

675,88

676,575

677,1660

678,691

679,1956

680,327

681,39

682,1850

683,251

684,1382

685,860

686,1800

687,581

688,639

689,348

690,3946

691,1746

692,761

693,381

694,2968

695,259

696,490

697,1800

698,403

699,198

700,1503

701,387

702,1202

703,250

704,354

705,3993

706,650

707,924

708,324

709,268

710,260

711,3310

712,840

713,1441

714,16

715,886

716,2467

717,2008

718,2486

719,228

720,1055

721,723

722,1837

723,191

724,1792

725,2250

726,917

727,1034

728,954

729,441

730,370

731,555

732,1013

733,837

734,303

735,709

736,821

737,2049

738,83

739,1226

740,3634

741,1075

742,157

743,325

744,861

745,1859

746,1096

747,4290

748,222

749,718

750,1250

751,200

752,1413

753,2344

754,2294

755,1506

756,2560

757,192

758,2093

759,649

760,397

761,18

762,106

763,3341

764,1859

765,1080

766,41

767,408

768,970

769,210

770,1801

771,147

772,1120

773,1867

774,799

775,378

776,892

777,24

778,274

779,3015

780,4692

781,15

782,1420

783,3948

784,581

785,59

786,594

787,2366

788,683

789,508

790,642

791,4815

792,506

793,1273

794,2486

795,760

796,1139

797,2727

798,359

799,1083

800,140

801,333

802,242

803,751

804,332

805,265

806,1650

807,1882

808,454

809,735

810,114

811,21

812,1089

813,486

814,422

815,2754

816,326

817,1192

818,230

819,94

820,2270

821,766

822,173

823,727

824,894

825,2190

826,724

827,1709

828,565

829,28

830,61

831,940

832,321

833,3849

834,97

835,95

836,526

837,886

838,609

839,439

840,82

841,2610

842,1322

843,1893

844,3183

845,1898

846,410

847,464

848,610

849,264

850,277

851,6024

852,226

853,1690

854,1462

855,217

856,853

857,515

858,2916

859,722

860,1097

861,128

862,745

863,317

864,3829

865,627

866,31

867,54

868,496

869,1340

870,227

871,662

872,1043

873,247

874,557

875,257

876,1685

877,2743

878,2456

879,98

880,30

881,886

882,1260

883,173

884,66

885,169

886,3948

887,642

888,573

889,3060

890,1059

891,421

892,213

893,320

894,2202

895,2998

896,406

897,467

898,307

899,1219

900,1741

901,1418

902,184

903,122

904,985

905,215

906,309

907,403

908,821

909,184

910,1832

911,111

912,331

913,1174

914,149

915,2917

916,351

917,499

918,590

919,440

920,1528

921,48

922,237

923,399

924,414

925,1438

926,5411

927,20

928,201

929,2054

930,1042

931,2335

932,52

933,357

934,2304

935,673

936,645

937,639

938,435

939,1257

940,1395

941,63

942,30

943,87

944,394

945,744

946,92

947,23

948,4472

949,123

950,397

951,2463

952,633

953,56

954,1398

955,2023

956,1521

957,273

958,1068

959,15

960,1226

961,2827

962,631

963,136

964,19

965,159

966,572

967,166

968,1420

969,80

970,874

971,399

972,1345

973,749

974,1696

975,421

976,315

977,250

978,1292

979,227

980,1027

981,1760

982,3754

983,359

984,795

985,811

986,942

987,34

988,1938

989,696

990,468

991,108

992,155

993,5688

994,235

995,241

996,716

997,151

998,848

999,1007

1000,17725

1001,4861

1002,6067

1003,28223

1004,2377

1005,5038

1006,1

1007,3837

1008,5344

1009,1287

1010,13893

1011,2227

1012,32786

1013,67

1014,18000

1015,23058

1016,2376

1017,1791

1018,1300

1019,5307

1020,9460

1021,67715

1022,5896

1023,16944

1024,17959

1025,3524

1026,2783

1027,3673

1028,13947

1029,1005

1030,164

1031,10591

1032,29533

1033,338

1034,103

1035,839

1036,24191

1037,4807

1038,15129

1039,247

1040,8021

1041,3400

1042,7041

1043,579

1044,2455

1045,6880

1046,2107

1047,6775

1048,18707

1049,5885

1050,4356

1051,5306

1052,3126

1053,36666

1054,9379

1055,18968

1056,29287

1057,6900

1058,15539

1059,2567

1060,7133

1061,5387

1062,1152

1063,7396

1064,12490

1065,8577

1066,6431

1067,6910

1068,16109

1069,29771

1070,14619

1071,4666

1072,1109

1073,19633

1074,3890

1075,14097

1076,418

1077,5859

1078,760

1079,7573

1080,17067

1081,3393

1082,3390

1083,17846

1084,19429

1085,21

1086,9131

1087,959

1088,18581

1089,3775

1090,1233

1091,2686

1092,8332

1093,2491

1094,4099

1095,21603

1096,9480

1097,3823

1098,2620

1099,2633

1100,1683

1101,5737

1102,10147

1103,3096

1104,5424

1105,16593

1106,14442

1107,3373

1108,5523

1109,9114

1110,2239

1111,64947

1112,10321

1113,5814

1114,4941

1115,2300

1116,18181

1117,7400

1118,556

1119,4448

1120,10843

1121,928

1122,3270

1123,9905

1124,16685

1125,10428

1126,6518

1127,53380

1128,6969

1129,14902

1130,16850

1131,7993

1132,18574

1133,12689

1134,4375

1135,18140

1136,6095

1137,6802

1138,15466

1139,7278

1140,33069

1141,1707

1142,9376

1143,42851

1144,57960

1145,524

1146,2934

1147,39266

1148,3879

1149,19143

1150,404

1151,13952

1152,19546

1153,13085

1154,1909

1155,8432

1156,7076

1157,16213

1158,22370

1159,8951

1160,14999

1161,8804

1162,7944

1163,33186

1164,3988

1165,597

1166,156

1167,14543

1168,6973

1169,12253

1170,2976

1171,1804

1172,4528

1173,382

1174,2234

1175,8659

1176,13746

1177,15938

1178,2880

1179,818

1180,1950

1181,9431

1182,7643

1183,16643

1184,7089

1185,2951

1186,10372

1187,2046

1188,15522

1189,19751

1190,1968

1191,890

1192,4406

1193,19425

1194,13118

1195,10640

1196,16435

1197,1766

1198,7661

1199,5326

1200,3421

1201,12355

1202,8713

1203,4804

1204,615

1205,4933

1206,12156

1207,398

1208,46399

1209,18619

1210,18663

1211,24309

1212,19531

1213,1583

1214,29275

1215,1115

1216,2832

1217,26690

1218,2963

1219,2706

1220,1819

1221,24517

1222,8243

1223,49971

1224,25302

1225,12571

1226,25049

1227,10112

1228,18638

1229,793

1230,11937

1231,12701

1232,4403

1233,2675

1234,1448

1235,8524

1236,16611

1237,5499

1238,3487

1239,3783

1240,8037

1241,7309

1242,1175

1243,10659

1244,1797

1245,721

1246,1474

1247,23123

1248,2998

1249,5287

1250,721

1251,32581

1252,37582

1253,11905

1254,10479

1255,2357

1256,4528

1257,8922

1258,5489

1259,14738

1260,11744

1261,518

1262,27839

1263,17191

1264,17571

1265,7564

1266,7307

1267,6178

1268,18646

1269,53118

1270,3176

1271,7233

1272,12223

1273,3655

1274,60

1275,10224

1276,907

1277,4378

1278,9770

1279,5188

1280,3723

1281,1286

1282,2619

1283,5354

1284,3264

1285,537

1286,9381

1287,368

1288,4949

1289,10882

1290,428

1291,6304

1292,1064

1293,9493

1294,2647

1295,13842

1296,21514

1297,7301

1298,16368

1299,48426

1300,11877

1301,94

1302,3869

1303,9122

1304,2710

1305,4120

1306,6915

1307,7104

1308,4428

1309,8982

1310,7028

1311,11040

1312,6575

1313,1357

1314,18739

1315,26449

1316,6553

1317,37584

1318,4261

1319,1868

1320,6676

1321,39400

1322,15148

1323,9639

1324,7062

1325,6504

1326,2864

1327,2368

1328,5111

1329,3380

1330,2468

1331,19589

1332,15392

1333,6705

1334,2861

1335,2234

1336,8605

1337,3348

1338,2717

1339,2120

1340,44584

1341,23548

1342,8106

1343,16352

1344,15632

1345,7887

1346,8638

1347,1214

1348,5294

1349,8508

1350,527

1351,2906

1352,19991

1353,3180

1354,17814

1355,1931

1356,1455

1357,6330

1358,6024

1359,10652

1360,4921

1361,22616

1362,8067

1363,14057

1364,10280

1365,31339

1366,18790

1367,9962

1368,19370

1369,62

1370,8972

1371,18336

1372,13728

1373,366

1374,8849

1375,111

1376,7608

1377,378

1378,9351

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1380,17101

1381,11273

1382,18683

1383,18693

1384,4867

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1386,23121

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1389,27625

1390,11113

1391,6507

1392,63

1393,1534

1394,27195

1395,5395

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1399,7074

1400,9144

1401,5405

1402,337

1403,14368

1404,4012

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1442,1948

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1465,6109

1466,530

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1468,14265

1469,5367

1470,21989

1471,4417

1472,75

1473,17313

1474,5440

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1476,11973

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1498,15593

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1500,8096

1501,2784

1502,5809

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1539,1819

1540,22328

1541,1950

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1595,6696

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1600,2246

1601,9327

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1900,6198

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1911,14924

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1914,14929

1915,4699

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1920,3927

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1922,965

1923,7521

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1930,877

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1932,14849

1933,1530

1934,10218

1935,3020

1936,1009

1937,13043

1938,2946

1939,17926

1940,2228

1941,14782

1942,1099

1943,16479

1944,8036

1945,28089

1946,644

1947,667

1948,7726

1949,1479

1950,32307

1951,52350

1952,6548

1953,3202

1954,4609

1955,8797

1956,243

1957,12198

1958,765

1959,584

1960,32160

1961,6115

1962,19566

1963,1221

1964,22514

1965,14588

1966,157

1967,40597

1968,21648

1969,1393

1970,6523

1971,12942

1972,2327

1973,1998

1974,10731

1975,6454

1976,11049

1977,2099

1978,6580

1979,17890

1980,1957

1981,10731

1982,8044

1983,8596

1984,11233

1985,401

1986,17237

1987,1828

1988,2249

1989,2791

1990,9332

1991,11769

1992,3056

1993,5320

1994,5546

1995,6922

1996,8876

1997,11671

1998,1899

1999,11815

2000,17354

2001,3432

2002,4407

2003,31435

2004,15910

2005,13665

2006,10343

2007,14919

2008,26051

2009,23159

2010,10758

2011,10499

2012,6616

2013,24960

2014,6919

2015,13278

2016,1668

2017,1154

2018,17080

2019,11987

2020,7318

2021,35401

2022,6758

2023,7278

2024,10830

2025,6995

2026,30930

2027,792

2028,1187

2029,23207

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2032,2189

2033,7410

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2035,1876

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2041,173

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2046,18054

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2058,40757

2059,2125

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2062,71

2063,14132

2064,1103

2065,3154

2066,4169

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2069,6956

2070,36338

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2073,6329

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2076,6293

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2100,1409

2101,1889

2102,2536

2103,5574

2104,16125

2105,19084

2106,10049

2107,4114

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2109,2534

2110,19101

2111,7669

2112,927

2113,6978

2114,22528

2115,3822

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2117,2123

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2119,2243

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2125,3285

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2130,4735

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2136,43781

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2142,13481

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2154,4511

2155,25601

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2157,40874

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2159,1372

2160,4104

2161,28694

2162,4505

2163,522

2164,8896

2165,28216

2166,27141

2167,19194

2168,1086

2169,4863

2170,9894

2171,10099

2172,6256

2173,4590

2174,1431

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2178,24493

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2188,75

2189,15415

2190,1078

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2192,4598

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2194,2423

2195,11494

2196,11252

2197,472

2198,348

2199,10342

2200,766

2201,5983

2202,6891

2203,10732

2204,20322

2205,7123

2206,29462

2207,8325

2208,1386

2209,5591

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2211,5120

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2213,4549

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2222,8753

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2240,1413

2241,10466

2242,9615

2243,846

2244,644

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2247,21201

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2249,10704

2250,19348

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2253,4104

2254,69437

2255,4141

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2257,2264

2258,16696

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2300,7905

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2302,1824

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2474,20505

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2480,42

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2500,16856

2501,13298

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2515,4990

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2524,22897

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2532,10076

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2540,1818

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2543,25734

2544,9069

2545,13026

2546,607

2547,3271

2548,13166

2549,5740

2550,6016

2551,4971

2552,8316

2553,3218

2554,23409

2555,16012

2556,509

2557,4385

2558,7902

2559,14916

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