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

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

Offset: 1

Author

Zak Seidov, Feb 19 2006

Keywords

• more
• nonn

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