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 1-5 of 5 results.

A116629 Positive integers k such that 13^k == 3 (mod k).

Original entry on oeis.org

1, 2, 5, 166, 287603, 9241538, 2366680105, 8347156585, 21682897793, 6988245760865, 9045859950329, 10076294257985, 50299408064905, 254874726648713
Offset: 1

Views

Author

Zak Seidov, Feb 19 2006

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Nov 24 2017
Some larger terms: 1440926367749746685, 76025040962646716305439353859479569558065. - Max Alekseyev, Jun 29 2011

Crossrefs

Cf. A116609, A050259, A122780, A130422, A123061, A277554.
Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), this sequence (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
    Join[{1, 2}, Select[Range[1, 5000], Mod[13^#, #] == 3 &]] (* G. C. Greubel, Nov 19 2017 *)
Join[{1, 2}, Select[Range[10000000], PowerMod[13, #, #] == 3 &]] (* Robert Price, Apr 10 2020 *)
  • PARI
    isok(n) = Mod(13, n)^n == 3; \\ Michel Marcus, Nov 19 2017

Extensions

Two more terms from Ryan Propper, Jan 09 2008
Terms 1,2 are prepended and a(9)-a(14) are added by Max Alekseyev, Jun 29 2011; Nov 24 2017

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

A277401 Positive integers n such that 7^n == 2 (mod n).

Original entry on oeis.org

1, 5, 143, 1133, 2171, 8567, 16805, 208091, 1887043, 517295383, 878436591673
Offset: 1

Views

Author

Seiichi Manyama, Oct 13 2016

Keywords

Comments

All terms are odd.
No other terms below 10^15. Some larger terms: 181204957971619289, 21305718571846184078167, 157*(7^157-2)/1355 (132 digits). - Max Alekseyev, Oct 18 2016

Examples

			7 == 2 mod 1, so 1 is a term;
16807 == 2 mod 5, so 5 is a term.

Crossrefs

Cf. A066438.
Cf. Solutions to 7^n == k (mod n): A277371 (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), this sequence (k=2), A277554 (k=3).
Cf. Solutions to b^n == 2 (mod n): A015919 (b=2), A276671 (b=3), A130421 (b=4), A124246 (b=5), this sequence (b=7), A116622 (b=13).

Programs

  • Mathematica
    Join[{1},Select[Range[5173*10^5],PowerMod[7,#,#]==2&]] (* The program will generate the first 10 terms of the sequence; it would take a very long time to generate the 11th term. *) (* Harvey P. Dale, Apr 15 2020 *)
  • PARI
    isok(n) = Mod(7, n)^n == 2; \\ Michel Marcus, Oct 13 2016

Formula

A066438(a(n)) = 2 for n > 1.

Extensions

a(10) from Michel Marcus, Oct 13 2016
a(11) from Max Alekseyev, Oct 18 2016

A277370 Positive integers k that divide 7^k + 2.

Original entry on oeis.org

1, 3, 15, 69, 2155, 34073, 876047637, 97090036327, 420397381695, 2125899832395, 3177544777277, 34434175473881, 40845965389135, 7267074621260963, 11720938824295035, 21419515204636141
Offset: 1

Views

Author

Seiichi Manyama, Oct 11 2016

Keywords

Comments

All terms are odd.
Some larger terms: 5623143546839445899891, 46186634668308298262543001. - Max Alekseyev, Oct 18 2016

Examples

			7^3 + 2 = 345 = 3 * 115, so 3 is a term.

Crossrefs

Cf. A066438.
Cf. Solutions to 7^n == k (mod n): A277371 (k=-3), this sequence (k=-2), A015954 (k=-1), A067947 (k=1), A277401 (k=2), A277554 (k=3).

Programs

  • Mathematica
    Select[Range[1, 9999, 2], Divisible[7^# + 2, #] &] (* Alonso del Arte, Oct 11 2016 *)
  • PARI
    is(n) = Mod(7, n)^n==-2 \\ Felix Fröhlich, Oct 14 2016

Formula

A066438(a(n)) = a(n) - 2 for n > 1.

Extensions

a(8)-a(13) from Max Alekseyev, Oct 18 2016
a(14)-a(16) from Max Alekseyev, Dec 27 2024

A277371 Positive integers k that divide 7^k + 3.

Original entry on oeis.org

1, 2, 4, 5, 26, 205, 2404, 88171, 1785134, 2010899, 58796834, 639723359, 657788549, 2050134685, 4809019972, 6114530474, 11931055777, 1292089439947, 1294667166242, 4586221808305
Offset: 1

Views

Author

Seiichi Manyama, Oct 11 2016

Keywords

Comments

No other terms below 10^15. Some larger terms: 68363072121992414, 95409505835353571, 1579273736555455916822694118995172, 5481414795965035698701145369881812, 14905708205837180834697194210878924, 45415365018055454586462673640490785681840279, 147329898999183698422689397719859437775766016038732177717811807964. - Max Alekseyev, Oct 18 2016

Examples

			7^5 + 3 = 16810 = 5 * 3362, so 5 is a term.

Crossrefs

Cf. A066438.
Cf. Solutions to 7^n == k (mod n): this sequence (k=-3), A277370 (k=-2), A015954 (k=-1), A067947 (k=1), A277401 (k=2), A277554 (k=3).

Programs

  • Mathematica
    Select[Range[10000], Divisible[7^# + 3, #] &] (* Alonso del Arte, Oct 11 2016 *)
Join[{1,2},Select[Range[21*10^5],PowerMod[7,#,#]==#-3&]] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Sep 21 2022 *)
  • PARI
    is(n) = Mod(7, n)^n==-3 \\ Felix Fröhlich, Oct 14 2016

Formula

A066438(a(n)) = a(n) - 3 for n > 2.

Extensions

a(15)-a(20) from Max Alekseyev, Oct 18 2016
Showing 1-5 of 5 results.

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

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