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

1,2

Comments

11 divides all except the first term.

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

Links

Table of n, a(n) for n=1..19.

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 *)

Crossrefs

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

Sequence in context: A128683 A292335 A177912 * A052782 A186249 A186250

Adjacent sequences: A128402 A128403 A128404 * A128406 A128407 A128408

Keyword

nonn,less

Author

Alexander Adamchuk, Mar 01 2007

Extensions

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

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

Status

approved