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

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

Offset: 1

Author

Zak Seidov, Feb 19 2006

Keywords

• more
• nonn

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