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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A015960 Numbers k such that k | 11^k + 1.

Original entry on oeis.org

1, 2, 3, 9, 27, 81, 111, 122, 243, 333, 729, 999, 2187, 2997, 4107, 6561, 7442, 8991, 10233, 12321, 13203, 19683, 24753, 26973, 30699, 36963, 39609, 59049, 74259, 80919, 89426, 92097, 110889, 118341, 118827, 151959, 177147, 222777
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), A015958 (b=10), this sequence (b=11), A015961 (b=12), A015963 (b=13), A015965 (b=14), A015968 (b=15), A015969 (b=16).
Cf. A333134.
Column k=11 of A333429.

Programs

  • Mathematica
    Select[Range[250000],PowerMod[11,#,#]==#-1&] (* Harvey P. Dale, Nov 09 2022 *)

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

A292338 Numbers k such that k^2 divides 13^k + 1.

Original entry on oeis.org

1, 7, 203, 11977, 154553, 353423, 4482037, 9904979, 20851957, 69262991, 264440183, 6824905927, 7803226417, 17244568439, 47773414171, 57280493557, 120586867331, 197922271883, 218692031341, 249815987281, 409580786629, 460390358603, 802768833013, 963574941161, 1003238606531, 1146808373599, 1385429010959, 1529257578289
Offset: 1

Views

Author

Max Alekseyev, Sep 16 2017

Keywords

Links

Crossrefs

Subsequence of A015963.
Cf. A128393, A177813.

A321364 Positive integers m such that 13^m == 12 (mod m).

Original entry on oeis.org

1, 13757837, 6969969233, 514208575135
Offset: 1

Views

Author

Max Alekseyev, Nov 07 2018

Keywords

Comments

No other terms below 10^15.
Some larger terms: 14551705803598782884189, 268766423508299769671017810348321281664525668552158231.

Crossrefs

Solutions to 13^m == k (mod m): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), A116611 (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), this sequence (k=12), A321365 (k=14), A116639 (k=15).
Cf. A116609, A127821, A128149.

Programs

A321365 Positive integers n such that 13^n == 14 (mod n).

Original entry on oeis.org

1, 5805311, 392908759, 399614833907, 2674764845549, 21997277871211, 67146783889057
Offset: 1

Views

Author

Max Alekseyev, Nov 08 2018

Keywords

Comments

No other terms below 10^15.

Crossrefs

Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), A116611 (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A321364 (k=12), this sequence (k=14), A116639 (k=15).
Cf. A116609, A127821, A128149, A128172.

Programs

Previous Showing 11-20 of 21 results. Next

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