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 1-3 of 3 results.

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

A333134 Positive integers k such that 11^k == 2 (mod k).

Original entry on oeis.org

1, 3, 413, 1329, 6587, 11629, 75761, 925071199, 9031140861789, 114876097917387, 1314252479257933
Offset: 1

Views

Author

Seiichi Manyama, Mar 20 2020

Keywords

Comments

No other terms below 10^16. Some larger terms: 1584680529929001639, 15598123298097725094806152851164088027801112472240274433891889912569153113. - Max Alekseyev, Jan 07 2025

Crossrefs

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=11), A116622 (b=13), A333269 (b=17).
Cf. A015960.

Programs

  • PARI
    for(k=1, 1e6, if(Mod(11, k)^k==2, print1(k", ")))

Extensions

a(9)-a(11) from Max Alekseyev, Jan 07 2025

A333414 Positive integers k such that k divides 17^k + 2.

Original entry on oeis.org

1, 19, 35, 115, 44095, 211117, 14376053, 43472060395, 561558718915, 2182879071661
Offset: 1

Views

Author

Seiichi Manyama, Mar 20 2020

Keywords

Comments

a(8) > 10^10.
a(11) > 4*10^12. - Giovanni Resta, Mar 22 2020

Crossrefs

Solutions to b^n == -2 (mod n): A015973 (b=3), A123062 (b=5), A277370 (b=7), A333413 (b=13), this sequence (b=17).
Cf. A333269.

Programs

  • PARI
    for(k=1, 1e6, if(Mod(17, k)^k==-2, print1(k", ")))

Extensions

a(8)-a(10) from Giovanni Resta, Mar 22 2020
Showing 1-3 of 3 results.