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

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

Offset

1,2

Comments

No other terms below 10^15. - Max Alekseyev, Nov 24 2017

Some larger terms: 1440926367749746685, 76025040962646716305439353859479569558065. - Max Alekseyev, Jun 29 2011

Links

Table of n, a(n) for n=1..14.

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 *)

Prog

(PARI) isok(n) = Mod(13, n)^n == 3; \\ Michel Marcus, Nov 19 2017

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)

Sequence in context: A263413 A270585 A041505 * A124275 A013130 A111392

Adjacent sequences: A116626 A116627 A116628 * A116630 A116631 A116632

Keyword

nonn

Author

Zak Seidov, Feb 19 2006

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

Status

approved