I numeri inferiori a 109 uguali alla somma di una potenza fissata delle loro cifre nelle basi da 2 a 20

La tabella seguente riporta i numeri inferiori a 109 uguali alla somma dei quadrati, dei cubi e dei biquadrati delle loro cifre in base b, escludendo il caso banale 1.

b \ n

2

3

4

3

123 = 5, 223 = 8

1223 = 17

-

4

-

204 = 8, 214 = 9, 1304 = 28, 1314 = 29, 2034 = 35, 2234 = 43, 3134 = 55, 3324 = 62

11034 = 83, 33034 = 243

5

235 = 13, 335 = 18

1035 = 28, 4335 = 118

21245 = 289, 24305 = 353, 31345 = 419

6

 

1506 = 66, 1516 = 67, 2436 = 99, 5146 = 190, 11556 = 251

-

7

137 = 10, 347 = 25, 447 = 32, 637 = 45

127 = 9, 227 = 16, 2507 = 133, 2517 = 134, 3057 = 152, 5057 = 250

-

8

248 = 20, 468 = 52

1348 = 92, 2058 = 133, 4638 = 307, 6608 = 432, 6618 = 433

208 = 16, 218 = 17, 4008 = 256, 4018 = 257, 4208 = 272, 4218 = 273

9

459 = 41, 559 = 50

309 = 27, 1509 = 126, 1519 = 127, 5709 = 468, 5719 = 469, 13889 = 1052

4329 = 353, 24469 = 1824

10

-

153, 370, 371, 407

1634, 8208, 9474

11

5611 = 61, 6611 = 72

3211 = 35, 10511 = 126, 30711 = 370, 70811 = 855, 96611 = 1161, A0611 = 1216, A6411 = 1280

24211 = 288, 800911 = 10657

12

2512 = 29, A512 = 125

57712 = 811, 66812 = 944, A8312 = 1539, 11AA12 = 2002

-

13

1413 = 17, 3613 = 45, 6713 = 85, 7713 = 98, A613 = 136, B413 = 160, B8513 = 1968

49013 = 793, 49113 = 794, 50913 = 854, 150A13 = 3052

396413 = 8194

14

 

13614 = 244, 40914 = 793

-

15

7815 = 113, 8815 = 128

C3A15 = 2755

1215 = 17, 2215 = 32, 177415 = 5059, E81915 = 49074, E82915 = 49089, 10BE415 = 53314

16

-

2116 = 35, 4016 = 64, 4116 = 65, 15616 = 342, 17316 = 371, 20816 = 520, 24816 = 584, 28516 = 645, 4A516 = 1189, 60B16 = 1547, 64B16 = 1611, 8C016 = 2240, 8C116 = 2241, 99A16 = 2458, AA916 = 2729, AC316 = 2755, CA816 = 3240, E6916 = 3689, EA016 = 3744, EA!16 = 3745, 152816 = 5416

B8D216 = 47314

17

2617 = 40, 3717 = 58, 8917 = 145, 9917 = 162, E717 = 245, F617 = 261

3317 = 54, 50B17 = 1456

76D817 = 36354

18

4818 = 80, 6918 = 117, C918 = 225, E818 = 260, G8918 = 5337

-

-

19

9A19 = 181, AA19 = 200, 58B19 = 1968, G8B19 = 5939

18019 = 513, 18119 = 514, 27819 = 863, 6D019 = 2413, 6D119 = 2414, 70D19 = 2540

CFA919 = 87922, FDD319 = 107828, 1GGAI19 = 246049

20

-

60D20 = 2413

6CA820 = 53808

 

La tabella seguente riporta i numeri inferiori a 109 uguali alla somma delle quinte, seste e settime potenze delle loro cifre in base b, escludendo il caso banale 1.

b \ n

5

6

7

3

10203 = 33, 10213 = 34, 21023 = 65

112123 = 131

1120223 = 386, 2002223 = 512

4

2004 = 32, 2014 = 33

321224 = 922

20004 = 128, 20014 = 129, 2100304 = 2316, 2100314 = 2317, 2120304 = 2444, 2120314 = 2445, 2200234 = 2571, 2220234 = 2699

5

22135 = 308

1240305 = 4890, 1240315 = 4891, 2424235 = 9113

20125 = 257

6

12326 = 308, 143406 = 2292, 143416 = 2293, 144326 = 2324, 235206 = 3432, 235216 = 3433, 444056 = 6197

4351526 = 36140

54352546 = 269458

7

1227 = 65, 43327 = 1542, 122057 = 3190, 122527 = 3222, 133507 = 3612, 133517 = 3613, 151247 = 4183, 360347 = 9286

2051457 = 35411

2134437 = 37271, 14245537 = 191334, 14335547 = 193393, 31265427 = 376889, 43556537 = 535069, 65156527 = 794376,

8

20408 = 1056, 20418 = 1057, 44238 = 2323, 406638 = 16819, 427108 = 17864, 427118 = 17865, 600078 = 24583, 620478 = 25639

6367038 = 212419

2008 = 128, 2018 = 129, 400008 = 16384, 400018 = 16385, 402008 = 16512, 402018 = 16513, 33520728 = 906298, 33522728 = 906426, 34514738 = 938811, 42176038 = 1122179, 77553368 = 2087646

9

3009 = 243, 3019 = 244, 120369 = 8052, 123369 = 8295, 144629 = 9857, 1088109 = 65538, 1088119 = 65539

554339 = 36804

30009 = 2187, 30019 = 2188, 22257649 = 1198372, 62758509 = 3357009, 62758519 = 3357010, 8870289 = 5300099

10

4150, 4151, 54748, 92727, 93084, 194979

548834

1741725, 4210818, 9800817, 9926315, 14459929

11

23011 = 275, 23111 = 276, 353411 = 4635, 551411 = 7275, 554211 = 7306, 603011 = 8019, 603111 = 8020, 1127011 = 16841, 1127111 = 16842, 1247011 = 17864, 1247111 = 17865, 2584011 = 36949, 2584111 = 36950, 4393511 = 63684, 4591511 = 66324, 4956311 = 71217, 6178811 = 90120, 6891011 = 99594, 6891111 = 99595, 9728811 = 141424, A827611 = 157383, 126A8911 = 199626, 18A2A911 = 291850

7263A011 = 1165098, 7263A111 = 1165099

319270311 = 5611015, 682941911 = 11959539

12

1476512 = 28733, 938A412 = 193084

36986212 = 887690, A2394A12 = 2536330

238029312 = 6884751, 58955A312 = 17116683, 114007BB12 = 39814271

13

464213 = 9856, 652513 = 14058, 2259313 = 62481, 5B35013 = 167544, 5B35113 = 167545, A3B2813 = 294094, B2A9313 = 320375, B33B313 = 323612, B51B313 = 325471, B533B13 = 325713, C34A213 = 350131, CA72313 = 365914, 115CB013 = 413010, 115CB113 = 413011

665B2913 = 2412003, 18BC75C13 = 8138948

101295213 = 4861352, 4661B7713 = 21710514, 90B0B0013 = 43757311, 90B0B0113 = 43757312, 9790C0513 = 46299414, A967C5313 = 51798568, AC9613813 = 52994053

14

74AB514 = 282007

-

153A63214 = 10362564

15

7995C15 = 386862, 829BB15 = 413951, A36BC15 = 517902

1A12EEC15 = 19045122

12215 = 257, 15095A615 = 15219156, 1977A5815 = 18605333, 350C01815 = 38009273, 37BB31615 = 40082196, 3813C6815 = 40310423, 38C418715 = 40868227, 428C49915 = 47527794, 8BCC89015 = 100128060, 8BCC89115 = 100128061, 8BCC92815 = 100128188, 9230CD715 = 104189152, 93D3C8015 = 105464820, 93D3C8115 = 105464821, A5E028715 = 118412452, C990C3D15 = 143980258, 101E881D15 = 172356328, 145E3AE415 = 220940089, 16CE840E15 = 249052289

16

2016 = 32, 2116 = 33, 40016 = 1024, 40116 = 1025, 42016 = 1056, 42116 = 1057, 5B016 = 1456, 5B116 = 1457, 600716 = 24583, 602716 = 24615, 640716 = 25607, 642716 = 25639, 800016 = 32768, 800116 = 32769, 802016 = 32800, 802116 = 32801, 840016 = 33792, 840116 = 33793, 842016 = 33824, 842116 = 33825, 1357916 = 79225, 2B70216 = 177922, 2B72216 = 177954, 5A07C16 = 368764, 5A47C16 = 369788, C00E016 = 786656, C00E116 = 786657, C04E016 = 787680, C04E116 = 787681, C60E716 = 811239, C64E716 = 812263, C80E016 = 819424, C80E116 = 819425, C84E016 = 820448, C84E116 = 820449, DE03016 = 909360, DE03116 = 909361, DE43016 = 910384, DE43116 = 910385, EB7C216 = 964546, FB06A16 = 1028202, FB46A16 = 1029226, FC27616 = 1032822, 104CF916 = 1068281, 10C8F916 = 1100025, 11CF9A16 = 1167258

97E42B16 = 9954347, EAD83B16 = 15390779

400016 = 16384, 400116 = 16385, 20008016 = 2097280, 20008116 = 2097281, 20408016 = 2113664, 20408116 = 2113665, 24860016 = 2393600, 24860116 = 2393601, 222C20016 = 35832320, 222C20116 = 35832321, DD5726E16 = 232092270, EE51BB416 = 249895860, 16F0E8E716 = 384887015

17

-

1B649517 = 2369380, 2808C217 = 3510400, 89F02017 = 12184274, 89F02117 = 12184275, 144BFG817 = 30209739

F73BF6A17 = 372311587, G55E6B417 = 393788701

18

-

CCE2EC18 = 24017088, 41462645

-

19

941519 = 63199, 234C819 = 282899, ADD7E19 = 1397217, B5GAB19 = 1473803, ICB8A19 = 2432219, 1H7I2H19 = 4746122

 

1874D4819 = 67799133, 5G4894019 = 275426470, 5G4894119 = 275426471, A3AFAAG19 = 479297018, FEC1HB219 = 741930660, GH17E0A19 = 795011177

20

4F10020 = 760400, 4F10120 = 760401

128HCI20 = 3591058, 1J1I1I20 = 6255238, E57CAI20 = 45661018, JA8FAB20 = 62470211

9DEC7H220 = 619939142

 

La tabella seguente riporta i numeri inferiori a 109 uguali alla somma delle ottave, none e decime potenze delle loro cifre in base b, escludendo il caso banale 1.

b \ n

8

9

10

3

1001203 = 258, 1001213 = 259

2012003 = 513, 2012013 = 514, 22102203 = 2049, 22102213 = 2050

11020003 = 1026, 11020013 = 1027, 121100203 = 3075, 121100213 = 3076, 121212123 = 4100

4

13022024 = 7330, 30310104 = 13124, 30310114 = 13125

200004 = 512, 200014 = 513, 110032124 = 20710, 110232124 = 21222, 213130204 = 40392, 213130214 = 40393

-

5

41122225 = 66562

403023325 = 322217, 4344344445 = 1874374

-

6

122222516 = 391907

5554350356 = 10067135

-

7

4223027 = 72865

250032427 = 2236488, 344541247 = 3021897, 524450027 = 4431562, 1255430557 = 8094840, 1613401447 = 10883814, 2546032557 = 16219922, 3361336147 = 20496270, 5426623267 = 32469576, 5652642267 = 34403018

123041227 = 1110699, 1500123327 = 9885773

8

321038 = 13379, 2004008 = 65792, 2004018 = 65793, 164506038 = 3821955, 637170058 = 13606405

2331733248 = 40695508

20008 = 1024, 20018 = 1025, 40000008 = 1048576, 40000018 = 1048577, 40020008 = 1049600, 40020018 = 1049601, 31156530678 = 423056951, 54772036048 = 637339524

9

127424529 = 6287267

300009 = 19683, 300019 = 19684, 210006309 = 10097892, 210006319 = 10097893, 210306309 = 10117575, 210306319 = 10117576, 210306309 = 3566148009 = 156608073, 3566148019 = 156608074

10333661709 = 403584750, 10333661719 = 403584751, 14557703429 = 586638974

10

24678050, 24678051, 88593477

146511208, 472335975, 534494836, 912985153

-

11

2426603911 = 46478562, A50634A611 = 203821954, A879902611 = 210315331

111520211 = 1954152, 3246625711 = 62744975, 8154665011 = 158541515, 8154665111 = 158541516, 19460320311 = 397800208, 39434679411 = 826098079

-

12

-

-

-

13

274755313 = 12383205, 4886941B13 = 292770723, 4A45A2A513 = 300912578

11862941913 = 919399061

-

14

-

-

-

15

12AA164015 = 201745410, 12AA164115 = 201745411

-

-

16

-

20016 = 512, 20116 = 513, 4000016 = 262144, 4000116 = 262145, 4020016 = 262656, 4020116 = 262657, 800000016 = 134217728, 800000116 = 134217729, 800020016 = 134218240, 800020116 = 134218241, 804000016 = 134479872, 804000116 = 134479873, 804020016 = 134480384, 804020116 = 134480385

-

17

-

-

-

18

-

-

-

19

-

1185997619 = 961443136

-

20

-

-

-