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.

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A015953 Numbers k such that k | 6^k + 1.

Original entry on oeis.org

1, 7, 49, 203, 343, 1379, 1421, 2401, 5887, 9653, 9947, 11977, 16807, 39991, 41209, 67571, 69629, 83839, 117649, 170723, 271663, 279937, 288463, 347333, 472997, 487403, 586873, 706643, 823543, 1159739, 1195061, 1901641, 1959559, 2019241, 2359469, 2431331
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Solutions to b^k == -1 (mod k): A006521 (b=2), A015949 (b=3), A015950 (b=4), A015951 (b=5), this sequence (b=6), A015954 (b=7), A015955 (b=8), A015957 (b=9), A015958 (b=10), A015960 (b=11), A015961 (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Column k=6 of A333429.

Programs

  • Mathematica
    Select[Range[2000000],PowerMod[6,#,#]==#-1&] (* Harvey P. Dale, Aug 28 2012 *)

A015955 Numbers k such that k | 8^k + 1.

Original entry on oeis.org

1, 3, 9, 27, 57, 81, 171, 243, 513, 729, 1083, 1539, 2187, 3249, 4401, 4617, 6561, 9747, 13203, 13851, 19683, 20577, 29241, 32547, 39609, 41553, 59049, 61731, 83619, 87723, 97641, 118179, 118827, 124659, 177147, 185193, 250857, 263169
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Solutions to b^k == -1 (mod k): A006521 (b=2), A015949 (b=3), A015950 (b=4), A015951 (b=5), A015953 (b=6), A015954 (b=7), this sequence (b=8), A015957 (b=9), A015958 (b=10), A015960 (b=11), A015961 (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Column k=8 of A333429.

A015957 Numbers k such that k | 9^k + 1.

Original entry on oeis.org

1, 2, 5, 25, 82, 125, 625, 2525, 3125, 3362, 5905, 12625, 15625, 29525, 63125, 78125, 137842, 147625, 188354, 255025, 315625, 375125, 390625, 738125, 1062625, 1275125, 1578125, 1875625, 1953125, 2982025, 3690625, 5313125, 5651522, 6375625, 6973805
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Solutions to b^k == -1 (mod k): A006521 (b=2), A015949 (b=3), A015950 (b=4), A015951 (b=5), A015953 (b=6), A015954 (b=7), A015955 (b=8), this sequence (b=9), A015958 (b=10), A015960 (b=11), A015961 (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Column k=9 of A333429.

Programs

  • Mathematica
    Select[Range[7*10^6],PowerMod[9,#,#]==#-1&] (* Harvey P. Dale, Apr 21 2024 *)

Extensions

More terms from David W. Wilson

A015958 Numbers k such that k | 10^k + 1.

Original entry on oeis.org

1, 11, 121, 253, 1331, 2783, 5819, 11891, 14641, 30613, 35167, 45023, 64009, 96569, 130801, 133837, 161051, 273493, 336743, 386837, 495253, 527197, 558877, 640343, 704099, 808841, 1035529, 1062259, 1438811, 1472207, 1652849, 1771561, 2221087, 3008423, 3045449
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Solutions to b^k == -1 (mod k): A006521 (b=2), A015949 (b=3), A015950 (b=4), A015951 (b=5), A015953 (b=6), A015954 (b=7), A015955 (b=8), A015957 (b=9), this sequence (b=10), A015960 (b=11), A015961 (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Column k=10 of A333429.

Programs

  • Mathematica
    Select[Range[15*10^5],PowerMod[10,#,#]==#-1&] (* Harvey P. Dale, Oct 01 2017 *)

Extensions

Corrected by T. D. Noe, Oct 31 2006

A015961 Positive integers k such that k | (12^k + 1).

Original entry on oeis.org

1, 13, 169, 1027, 2197, 13351, 28561, 81133, 173563, 371293, 468481, 685633, 1054729, 2256319, 2890927, 4826809, 6090253, 6409507, 8913229, 13711477, 29332147, 37009999, 37582051, 54165007, 62748517, 79173289, 83323591, 115871977, 178249201, 228383233
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Crossrefs

Solutions to b^k == -1 (mod k): A006521 (b=2), A015949 (b=3), A015950 (b=4), A015951 (b=5), A015953 (b=6), A015954 (b=7), A015955 (b=8), A015957 (b=9), A015958 (b=10), A015960 (b=11), this sequence (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Column k=12 of A333429.

Extensions

More terms from Max Alekseyev, Aug 01 2011
a(30) from Jon E. Schoenfield, Aug 27 2021

A015969 Numbers k that divide 16^k + 1.

Original entry on oeis.org

1, 17, 289, 4913, 83521, 1419857, 6029713, 12027313, 24137569, 85525793, 102505121, 204464321, 410338673, 1453938481, 1742587057, 3475893457, 6975757441, 24716954177, 29623979969, 59090188769, 111612202577, 118587876497, 420188221009, 500540685121, 503607659473
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Cf. A006521, A015949, A015950, A015951, A015953, A015954, A015955, A015957, A015958, A015960, A015961, A015963, A015965, A015968, A014957.
Column k=16 of A333429.

Extensions

More terms from Max Alekseyev, Oct 02 2010
Missing terms a(10), a(14), a(18), and a(23) from Giovanni Resta, Mar 23 2020

A123061 Numbers k that divide 5^k - 3.

Original entry on oeis.org

1, 2, 22, 77, 242, 371, 16102, 45727, 73447, 81286, 112277, 368237, 10191797, 13563742, 30958697, 389974222, 6171655457, 55606837682, 401469524477, 434715808966, 1729670231597, 12399384518278, 28370781933478, 32458602019394, 45360785149757, 1073804398767214
Offset: 1

Views

Author

Alexander Adamchuk, Nov 04 2006

Keywords

Comments

Some larger terms: 10157607413638637338691, 678641208236297002873422185407157785099272404809011007522511134591325167. - Max Alekseyev, Oct 20 2016

Crossrefs

Cf. A050259, A130422, A277554, A116629.
Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), this sequence (k=3), A123052 (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    Select[Range[1000000], IntegerQ[(PowerMod[5,#,# ]-3)/# ]&]
Do[If[IntegerQ[(PowerMod[5, n, n ]-3)/n], Print[n]], {n, 10^9}] (* Ryan Propper, Dec 30 2006 *)
  • PARI
    is(n)=Mod(5,n)^n==3 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

More terms from Farideh Firoozbakht, Nov 18 2006
Corrected and extended by Ryan Propper, Jan 01 2007
Entry revised by N. J. A. Sloane, Jan 24 2007
a(18) from Lars Blomberg, Dec 12 2011
a(19)-a(26) from Max Alekseyev, Oct 20 2016

A123052 Numbers k that divide 5^k + 3.

Original entry on oeis.org

1, 2, 4, 14, 628, 11524, 16814, 188404, 441484, 2541014, 3984724, 172315684, 208268941, 40874725514, 280454588548, 489850370956, 1235856817732, 62479203805793, 95467808763364, 116016015619396, 396249210287836
Offset: 1

Views

Author

Alexander Adamchuk, Nov 04 2006

Keywords

Comments

No other terms below 10^15. A larger term: 783847656467936404. - Max Alekseyev, Oct 16 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), this sequence (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    Select[Range[1000000], IntegerQ[(PowerMod[5,#,# ]+3)/# ]&]
  • PARI
    is(n)=Mod(5,n)^n==-3 \\ Charles R Greathouse IV, Apr 06 2014

Extensions

a(10)-a(13) from Ryan Propper, Dec 30 2006, Jan 02 2007
More terms from Lars Blomberg, Nov 25 2011
Terms a(14) onwards were reported incorrect by Toshitaka Suzuki, and have been deleted. - N. J. A. Sloane, Mar 18 2014
a(14)-a(17) from Toshitaka Suzuki, Mar 18 2014, Apr 03 2014
a(18)-a(21) from Max Alekseyev, Oct 16 2016

A125949 Numbers k that divide 5^k - 4.

Original entry on oeis.org

1, 4769, 8563651, 300414792131, 2353957351049, 15960089894129, 452045914836301, 657236915690111
Offset: 1

Views

Author

Alexander Adamchuk, Feb 04 2007

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 17 2016

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), A123052 (k=-3), this sequence (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

  • Mathematica
    a(1) = 1; Do[ If[ PowerMod[5, 2n - 1, 2n - 1] - 4 == 0, Print[2n - 1]], {n,10^9}]
  • PARI
    is(n)=Mod(5,n)^n==4 \\ Charles R Greathouse IV, May 15 2013

Extensions

a(4)-a(8) from Max Alekseyev, Jun 09 2010, Oct 17 2016

A277350 Positive integers n such that 5^n == 6 (mod n).

Original entry on oeis.org

1, 15853, 5520343, 111966563, 2232207889, 5551501871
Offset: 1

Views

Author

Seiichi Manyama, Oct 10 2016

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 18 2016

Crossrefs

Cf. Solutions to 5^n == k (mod n): A277348 (k=-6), A015891 (k=-5), A123047 (k=-4), A123052 (k=-3), A123062 (k=-2), A015951 (k=-1), A067946 (k=1), A124246 (k=2), A123061 (k=3), A125949 (k=4), A123091 (k=5), this sequence (k=6).

Programs

Previous Showing 11-20 of 23 results. Next

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

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