cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 27 results. Next

A127106 Numbers k such that k^2 divides 6^k-1.

Original entry on oeis.org

1, 5, 1555, 9673655, 187159211791705, 776119592182705
Offset: 1

Views

Author

Alexander Adamchuk, Jan 05 2007

Keywords

Comments

Subsequence of A014946.

Crossrefs

Cf. A127100, A127101, A127102, A127103, A127104, A127105, A127107, A127092, A014946.

Programs

  • Mathematica
    Select[Range[20000], IntegerQ[(PowerMod[6, #, #^2 ]-1)/#^2 ]&]

Extensions

Two more terms from Max Alekseyev, May 05 2010

A127102 Numbers k such that k^2 divides 8^k-1.

Original entry on oeis.org

1, 7, 889, 2359, 299593, 2033143, 13549249, 42931441, 100170217, 310935751, 685169191, 3606045247, 4566096913, 5452293007, 6620620783, 12721617559, 30987132463, 65576560063, 92349997537, 104785348087, 457967746369
Offset: 1

Views

Author

Alexander Adamchuk, Jan 05 2007, Jan 07 2007

Keywords

Comments

Subsequence of A014949.
a(5) = 299593 = (8^7-1)/7 is a repunit in base 8, 1111111(base 8). The first 5 listed terms of a(n) are terms of the finite sequence A003530: divisors of 8^7-1. [Corrected and edited by M. F. Hasler, Nov 21 2018]
Also a subsequence of A177908, see there for more comments on properties of terms of this sequence. - M. F. Hasler, Nov 21 2018

Crossrefs

Cf. A127100, A127101, A127103, A127104, A127105, A127106, A127107, A127092, A014949, A003530.

Programs

  • Mathematica
    Select[Range[20000], IntegerQ[(PowerMod[8, #, #^2 ]-1)/#^2 ]&]
  • PARI
    is(n)=Mod(8,n^2)^n==1 \\ M. F. Hasler, Nov 21 2018

Extensions

More terms from Ryan Propper, Jan 05 2007
Terms a(12) onward from Max Alekseyev, May 06 2010

A127100 Numbers k such that k^2 divides 10^k-1.

Original entry on oeis.org

1, 3, 9, 111, 333, 3003003, 111111111, 225121209, 675363627, 27486820443, 32119664517, 82460461329, 24048075051027, 90180273183093, 225346555330209, 889778776887999, 3336670107774441, 10717272100393839, 19885751580714849, 27514334750263443
Offset: 1

Views

Author

Alexander Adamchuk, Jan 05 2007, Jan 07 2006

Keywords

Comments

Subsequence of A014950.
First 7 terms are palindromes. a(n) is divisible by 3 for 1Alexander Adamchuk, Jan 25 2007
Except for 3, also numbers n such that the decimal expansion of 1/n^2 has period n. - Arkadiusz Wesolowski, Mar 13 2012

Crossrefs

Cf. A127101, A127102, A127103, A127104, A127105, A127106, A127107, A127092, A014950.

Programs

  • Mathematica
    Select[Range[20000], IntegerQ[(PowerMod[10, #, #^2 ]-1)/#^2 ]&]

Extensions

More terms from Ryan Propper, Jan 06 2007
Further terms and edited by Max Alekseyev, May 09 2010

A127092 Numbers k such that k^2 divides 11^k - 1.

Original entry on oeis.org

1, 2, 4, 5, 6, 10, 12, 20, 30, 42, 60, 84, 114, 156, 210, 222, 228, 244, 420, 444, 570, 732, 780, 798, 930, 1092, 1110, 1140, 1220, 1554, 1596, 1806, 1860, 2220, 2436, 2964, 3108, 3612, 3660, 3990, 4218, 5124, 5460, 5772, 6510, 7770, 7980, 8268, 8436, 9030
Offset: 1

Views

Author

Alexander Adamchuk, Jan 05 2007

Keywords

Comments

Subsequence of A068383.

Links

Crossrefs

Column k=11 of A333500.
Cf. A068383, A127100, A127101, A127102, A127104, A127105, A127106, A127107, A292336.

Programs

  • Mathematica
    Select[Range[15000], IntegerQ[(PowerMod[11, #, #^2 ]-1)/#^2 ]&]
Join[{1},Select[Range[9100],PowerMod[11,#,#^2]==1&]] (* Harvey P. Dale, Dec 30 2018 *)
  • PARI
    for(k=1, 1e4, if(Mod(11, k^2)^k==1, print1(k", "))) \\ Seiichi Manyama, Mar 25 2020

A127103 Numbers k such that k^2 divides 3^k-1.

Original entry on oeis.org

1, 2, 4, 20, 220, 1220, 2420, 5060, 13420, 14740, 23620, 55660, 145420, 147620, 162140, 237820, 259820, 290620, 308660, 339020, 447740, 847220, 899140, 1210220, 1440820, 1599620, 1759340, 2332660, 2616020, 2858020, 3196820, 3344660
Offset: 1

Views

Author

Alexander Adamchuk, Jan 05 2007

Keywords

Comments

From Alexander Adamchuk, Jan 11 2007: (Start)
2 divides a(n) for n>1. 2^2 divides a(n) for n>2. 5 divides a(n) for n>3.
11 divides a(n) for n = {5,7,8,9,10,12,13,14,15,16,17,18,19,20,22,23,24,26,27, 28,29,30,31,31,33,34,35,...}.
11^2 divides a(n) for n = {7,12,14,15,26,27,29,30,31,33,34,...}.
Prime factors of a(n) in order of their appearance in a(n) are {2,5,11,61,23,67,1181,661,47,1321,367,3851,5501,727,461,269,...}. (End)

Links

Crossrefs

Subset of A067945 (numbers k that divide 3^k - 1).
Cf. A127100, A127101, A127102, A127104, A127105, A127106, A127107, A127092.

Programs

  • Mathematica
    Select[Range[30000], IntegerQ[(PowerMod[3, #, #^2 ]-1)/#^2 ]&]
Join[{1},Select[Range[335*10^4],PowerMod[3,#,#^2]==1&]] (* Harvey P. Dale, Oct 02 2019 *)
  • PARI
    is(k) = Mod(3, k^2)^k == 1; \\ Amiram Eldar, May 21 2024

Extensions

More terms from Ryan Propper and Alexander Adamchuk, Jan 05 2007

A128393 Numbers k such that k^2 divides 13^k - 1.

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 14, 20, 28, 42, 60, 68, 84, 140, 183, 204, 220, 340, 366, 406, 420, 476, 660, 732, 812, 942, 1020, 1218, 1428, 1540, 1806, 1860, 1884, 2380, 2436, 2562, 3612, 3660, 3740, 4060, 4620, 5060, 5124, 6594, 7004, 7140, 8420, 9420, 9940, 11220
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • Mathematica
    Join[{1},Select[Range[12000],PowerMod[13,#,#^2]==1&]] (* Harvey P. Dale, Sep 05 2012 *)

A128397 Numbers k such that k^2 divides 17^k-1.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 36, 40, 42, 48, 60, 72, 78, 80, 84, 116, 120, 126, 144, 156, 168, 180, 220, 232, 234, 240, 252, 312, 336, 342, 348, 360, 420, 440, 464, 468, 504, 546, 580, 624, 660, 684, 696, 720, 780, 840, 880, 936, 1008, 1044, 1092, 1160
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Comments

The first 9 numbers (and many more) which are a multiple of their digital sum in all bases from 2 through 16 (A218087), are members of this sequence, and also of A177917. - M. F. Hasler, Oct 22 2012

Links

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128398, A128399, A128400, A128401, A128402, A128403, A128404.
Cf. A177917.

Programs

A128398 Numbers k such that k^2 divides 18^k - 1.

Original entry on oeis.org

1, 17, 128583032925805678351
Offset: 1

Views

Author

Alexander Adamchuk, Mar 08 2007

Keywords

Comments

17 divides a(n) for n > 1.
a(4) > 10^50. - Max Alekseyev, Mar 01 2025

Crossrefs

Subsequence of A128358.
Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

A128399 Numbers k such that k^2 divides 19^k-1.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 10, 12, 18, 20, 30, 36, 42, 60, 84, 90, 110, 126, 156, 180, 210, 220, 252, 294, 330, 381, 420, 468, 588, 630, 660, 724, 762, 780, 882, 930, 990, 1092, 1143, 1260, 1332, 1470, 1510, 1524, 1764, 1806, 1830, 1860, 1980, 2028, 2058, 2172, 2286, 2310
Offset: 1

Views

Author

Alexander Adamchuk, Mar 01 2007

Keywords

Links

Crossrefs

Columns k=19 of A333500.
Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128400, A128401, A128402, A128403, A128404.

Programs

  • Mathematica
    Join[{1},Select[Range[3000],PowerMod[19,#,#^2]==1&]] (* Harvey P. Dale, Oct 24 2017 *)
  • PARI
    for(k=1, 1e4, if(Mod(19, k^2)^k==1, print1(k", "))) \\ Seiichi Manyama, Mar 25 2020

A128400 Numbers k such that k^2 divides 20^k - 1.

Original entry on oeis.org

1, 19, 1432001198261, 3661225986659, 275941052631578947368421, 43838606653900416716028459121, 26357241068661238901986943659181
Offset: 1

Views

Author

Alexander Adamchuk, Mar 08 2007

Keywords

Comments

19 divides a(n) for n > 1.
Subsequence of A128360.

Crossrefs

Cf. A128360, A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128405, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

  • PARI
    for( n=1, 10^6, Mod(20,n^2)^n - 1 || print1(n",")) \\ M. F. Hasler, Oct 20 2008

Extensions

a(4) from Max Alekseyev, Oct 18 2008
a(5)-a(7) from Max Alekseyev, May 06 2010
Showing 1-10 of 27 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.