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%I #29 Mar 30 2020 03:46:44
%S 1,3,5,185,2199,14061,5672119,6719547,192178873,913591893,4589621727,
%T 9762178659,1157052555699
%N Positive integers k such that k divides 13^k + 2.
%C a(14) > 6*10^12. - _Giovanni Resta_, Mar 29 2020
%t Select[Range[100000], Divisible[PowerMod[13, #, #] + 2, #] &] (* _Jinyuan Wang_, Mar 28 2020 *)
%o (PARI) for(k=1, 1e6, if(Mod(13, k)^k==-2, print1(k", ")))
%Y 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).
%Y Solutions to b^k == -2 (mod k): A015973 (b = 3), A123062 (b = 5), A277370 (b = 7), this sequence (b = 13), A333414 (b = 17).
%K nonn,more
%O 1,2
%A _Seiichi Manyama_, Mar 20 2020
%E a(13) from _Giovanni Resta_, Mar 29 2020