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 16 results. Next

A015963 Numbers k such that k | 13^k + 1.

Original entry on oeis.org

1, 2, 7, 10, 34, 49, 50, 170, 203, 250, 343, 578, 850, 1250, 1421, 2401, 2890, 4210, 4250, 5887, 6010, 6250, 6410, 9826, 9947, 11977, 14450, 16807, 21050, 21250, 30050, 31250, 32050, 34714, 41209, 49130, 69629, 71570, 72250, 83839, 102170
Offset: 1

Views

Author

Robert G. Wilson v

Keywords

Links

Crossrefs

Solutions to 13^n == k (mod n): this sequence (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), A116639 (k=15).
Column k=13 of A333429.

Programs

  • Mathematica
    Select[Range[102170], Divisible[13^# + 1, #] &] (* Robert Price, Apr 10 2020 *)

A116622 Positive integers n such that 13^n == 2 (mod n).

Original entry on oeis.org

1, 11, 140711, 863101, 1856455, 115602923, 566411084209, 706836043419179
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^16. - Max Alekseyev, Nov 02 2018

Crossrefs

Cf. A116609.
Solutions to b^n == 2 (mod n): A015919 (b=2), A276671 (b=3), A130421 (b=4), A124246 (b=5), A277401 (b=7), this sequence (b=13), A333269 (b=17).
Solutions to 13^n == k (mod n): A015963 (k=-1), A116621 (k=1), this sequence (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), A116639 (k=15).

Programs

  • Mathematica
    Select[Range[1, 500000], Mod[13^#, #] == 2 &] (* G. C. Greubel, Nov 19 2017 *)
Join[{1}, Select[Range[5000000], PowerMod[13, #, #] == 2 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 2; \\ Michel Marcus, Nov 19 2017

Extensions

One more term from Ryan Propper, Jun 11 2006
Term a(1)=1 is prepended and a(7)-a(8) are added by Max Alekseyev, Jun 29 2011

A116611 Positive integers n such that 13^n == 5 (mod n).

Original entry on oeis.org

1, 2, 4, 44, 82, 236, 25433, 177764, 219244, 86150213, 107218402, 1260236441, 12856300141, 447650116364, 657175627369, 14543842704596, 125035120614917
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15.
Some larger terms: 99790373907467602, 846248577183963835642742, 273781047810302314432122404459324, 4174626353309446327489382394518975030641698849116, 211*(13^211-5)/12607932861823674049268705845744 (207 digits). - Max Alekseyev, Jun 29 2011

Examples

			44 is in this sequence because 13^44 = 10315908977942302627204470186314316211062255002161 = 234452476771415968800101595143507186615051250049*44 + 5 == 5 (mod 44).

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), this sequence (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A116639 (k=15).
Cf. A116609, A128121, A276740, A123091.

Programs

  • Mathematica
    Join[{1, 2}, Select[Range[1000000], PowerMod[13, #, #] == 5 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    is(n) = Mod(13,n)^n==5; \\ Charles R Greathouse IV, Jun 08 2015

Extensions

More terms from Ryan Propper, Apr 01 2006
Terms 1,2,4 are prepended and a(13)-a(17) are added by Max Alekseyev, Jun 29 2011, Nov 27 2017

A116620 Positive integers n such that 13^n == 10 (mod n).

Original entry on oeis.org

1, 3, 9, 74853, 1275039, 27181907, 31261887, 989255061, 4813809711, 3187842157567, 313768710194691
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Nov 06 2018
9909932321420413420533943 is a term. - Max Alekseyev, Jun 29 2011

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), this sequence (k=10), A116638 (k=11), A116639 (k=15).
Cf. A116609.

Programs

  • Mathematica
    Join[{1, 3, 9}, Select[Range[2000000], PowerMod[13, #, #] == 10 &]] (* Robert Price, Apr 10 2020 *)

Extensions

More terms from Ryan Propper, Jun 12 2006
Terms 1,3,9 prepended and a(10)-a(11) added by Max Alekseyev, Jun 29 2011, Nov 06 2018

A116630 Positive integers n such that 13^n == 4 (mod n).

Original entry on oeis.org

1, 3, 51, 129, 125869, 158287, 1723647, 1839003, 90808797, 3661886147, 7368982721, 130424652229, 1616928424359, 4003183891851, 66657658685869
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Nov 26 2017
Some larger terms: 84058689739550643018360088224267, 11083544368708558891212925543084197628431243723. - Max Alekseyev, Jun 26 2011

Crossrefs

Solutions to 13^n == k (mod n): A001022 (k=0), A015963(k=-1), A116621 (k=1), A116622 (k=2), A116629(k=3), this sequence (k=4), A116611 (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A116639 (k=15)
Cf. A116609, A015921, A125949.

Programs

  • Mathematica
    Join[{1, 3}, Select[Range[1, 5000], Mod[13^#, #] == 4 &]] (* G. C. Greubel, Nov 19 2017 *)
Join[{1, 3}, Select[Range[2000000], PowerMod[13, #, #] == 4 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 4; \\ Michel Marcus, Nov 19 2017

Extensions

More terms from Ryan Propper, Jan 09 2008
Terms 1,3 prepended and a(12)-a(15) added by Max Alekseyev, Jun 26 2011, Nov 26 2017

A116631 Positive integers n such that 13^n == 6 (mod n).

Original entry on oeis.org

1, 7, 8743, 50239, 312389, 8789977, 87453889, 96301009, 3963715129, 5062673539, 6854133309107, 16987071590111, 72278468169733, 411419589731633, 590475819370933
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. A large term: 2455610470454186971078168169. - Max Alekseyev, Dec 19 2017

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), this sequence (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A116639 (k=15).
Cf. A116609, A128122, A277628, A277350.

Programs

  • Mathematica
    Join[{1}, Select[Range[1, 9000], Mod[13^#, #] == 6 &]] (* G. C. Greubel, Nov 19 2017 *)
Join[{1}, Select[Range[10000000], PowerMod[13, #, #] == 6 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 6; \\ Michel Marcus, Nov 19 2017

Extensions

More terms from Ryan Propper, Mar 30 2007
Term 1 is prepended and a(11)-a(15) added by Max Alekseyev, Jun 29 2011, Dec 19 2017

A116632 Positive integers n such that 13^n == 7 (mod n).

Original entry on oeis.org

1, 2, 3, 6, 15, 75, 219, 1335, 3246, 4975, 5475, 7775, 8922, 28614, 67675, 69998, 103135, 313609, 548983, 624193, 6539595, 13193562, 26383395, 111892866, 315953675, 5330142066, 33738816835, 66899423586, 336966134829, 645835313441, 742199683475, 1244107219389, 10187548490537, 760354210440662
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Oct 30 2018
Some larger terms: 6584692157923407917184426, 3226231185229904054184099310127719809, 30643479515551752620928357020812679775, 5890087594520845596744547263586007316572563275. - Max Alekseyev, Oct 30 2018

Crossrefs

Cf. A116609, A116611, A116620, A116621, A116622, A116629, A116630, A116631.

Programs

  • Mathematica
    Join[{1, 2, 3, 6}, Select[Range[1, 9000], Mod[13^#, #] == 7 &]] (* G. C. Greubel, Nov 19 2017 *)
Join[{1, 2, 3, 6}, Select[Range[10000000], PowerMod[13, #, #] == 7 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 7; \\ Michel Marcus, Nov 19 2017

Extensions

More terms from Ryan Propper, Mar 30 2007
Terms 1,2,3,6 prepended and a(27)-a(34) added by Max Alekseyev, Jun 30 2011, Oct 30 2018

A116636 Positive integers k such that 13^k == 9 (mod k).

Original entry on oeis.org

1, 2, 4, 8, 10, 172, 296, 332, 410, 872, 1048, 1070, 1544, 2830, 3470, 7486, 9196, 22184, 90892, 121174, 299816, 575206, 885112, 1329388, 1386430, 2518994, 4167272, 5600212, 8475016, 9180370, 12348446, 18483076, 19185890, 20806274, 28984094, 37114141
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

For k > 9 in this sequence, A116609(k) = 9. - Iain Fox, Nov 20 2017

Links

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), this sequence (k=9), A116620 (k=10), A116638 (k=11), A116639 (k=15).
Cf. A116609.

Programs

  • Mathematica
    Join[{1, 2, 4, 8}, Select[Range[1, 9000], Mod[13^#, #] == 9 &]] (* G. C. Greubel, Nov 19 2017 *)
Join[{1,2,4,8},Select[Range[38*10^6],PowerMod[13,#,#]==9&]] (* Harvey P. Dale, Jul 06 2025 *)
  • PARI
    isok(n) = Mod(13, n)^n == 9; \\ Michel Marcus, Nov 19 2017

Extensions

More terms from Ryan Propper, Nov 05 2006
Terms 1,2,4,8 prepended by Max Alekseyev, Jun 28 2011

A116638 Positive integers n such that 13^n == 11 (mod n).

Original entry on oeis.org

1, 2, 158, 301823, 1851103, 8616098, 60528467, 1087582634, 1628818307, 16205558969
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Nov 07 2018
Large terms: 38763675625170712166, 527929122195463909516681113715859203.

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), this sequence (k=11), A116639 (k=15).
Cf. A116609.

Programs

  • Mathematica
    Join[{1, 2}, Select[Range[1, 9000], Mod[13^#, #] == 11 &]] (* G. C. Greubel, Nov 20 2017 *)
Join[{1, 2}, Select[Range[10000000], PowerMod[13, #, #] == 11 &]] (* Robert Price, Apr 10 2020 *)

Extensions

More terms from Ryan Propper, Jan 11 2008
Edited by Max Alekseyev, May 04 2010

A116639 Numbers n such that 13^n == 15 (mod n).

Original entry on oeis.org

1, 2, 14, 22, 1582, 11266, 52766, 76202, 100562, 494371, 641141, 1698494, 66593158, 469296521, 10917186079, 12062558662, 4928050067287, 5315948729617, 29841213777637, 113215787397262, 778590786358582, 787324867879046
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. Some large terms: 6991413003775539262, 2360895769139218729155198091. - Max Alekseyev, Oct 15 2016

Crossrefs

Cf. A116609, A116611, A116620, A116621, A116622, A116629, A116630, A116631, A116632, A116636, A116638.

Programs

  • Mathematica
    Select[Range[25000000],PowerMod[13,#,# ]==15&] (* Harvey P. Dale, Feb 03 2009 *)

Extensions

One more term from Harvey P. Dale, Feb 03 2009
Edited by Max Alekseyev, Sep 19 2009
a(14)-a(22) from Max Alekseyev, May 04 2010, Apr 29 2014, Oct 15 2016
Showing 1-10 of 16 results. Next

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