A333413 Positive integers k such that k divides 13^k + 2.

1, 3, 5, 185, 2199, 14061, 5672119, 6719547, 192178873, 913591893, 4589621727, 9762178659, 1157052555699

Offset: 1

Author

Seiichi Manyama, Mar 20 2020

Keywords

• nonn
• more

Comments

a(14) > 6*10^12. - Giovanni Resta, Mar 29 2020

Crossrefs

Solutions to 13^k == m (mod k): this sequence (m = -2), A015963 (m = -1), A116621 (m = 1), A116622 (m = 2), A116629 (m = 3), A116630 (m = 4), A116611 (m = 5), A116631 (m = 6), A116632 (m = 7), A295532 (m = 8), A116636 (m = 9), A116620 (m = 10), A116638 (m = 11), A116639 (k = 15).

Solutions to b^k == -2 (mod k): A015973 (b = 3), A123062 (b = 5), A277370 (b = 7), this sequence (b = 13), A333414 (b = 17).

Programs

Mathematica

Select[Range[100000], Divisible[PowerMod[13, #, #] + 2, #] &] (* Jinyuan Wang, Mar 28 2020 *)

PARI

for(k=1, 1e6, if(Mod(13, k)^k==-2, print1(k", ")))

Extensions

a(13) from Giovanni Resta, Mar 29 2020