A128405 Numbers k such that k^2 divides 12^k - 1.

1, 11, 253, 11891, 768361, 36112967, 61488361, 154261943, 2936791979, 61057324141, 67546215517, 107342336783, 186740152357, 347036920549, 429306186947, 468493520891, 635974117823, 797688507253, 3174672129299

Offset: 1

Author

Alexander Adamchuk, Mar 01 2007

Keywords

• nonn
• less

Comments

11 divides all except the first term.

All terms are congruent to +-1 (mod 12). - Robert G. Wilson v, Dec 19 2014

Crossrefs

Cf. A127103, A127104, A127105, A127106, A127107, A127102, A127101, A127100, A127092, A128393, A128394, A128395, A128396, A128397, A128398, A128399, A128400, A128401, A128402, A128403, A128404.

Programs

Mathematica

fQ[n_] := Mod[ PowerMod[12, n, n^2] - 1, n^2] == 0; k = 1; lst = {}; While[k < 100000001, If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k += 10; If[ fQ@ k, AppendTo[lst, k]; Print@ k]; k += 2]; lst (* Robert G. Wilson v, Dec 19 2014 *)

Extensions

a(6)-a(8) from Farideh Firoozbakht, Mar 05 2007

Terms a(9) onward from Max Alekseyev, May 06 2010