A128685 Numbers k such that k^3 divides 12^(k^2) + 1.

1, 13, 1027, 52741, 468481, 2890927, 4166539, 37009999, 228383233, 999884119, 1345997497, 1900627417, 2126334691, 4499474941, 5037873529, 11728490839, 104180336299, 105897267463, 150149565943, 926550776281, 4056529870783

Offset

1,2

Comments

13 divides a(n) for n > 1.

Links

Table of n, a(n) for n=1..21.

Mathematica

Select[Range[5*10^6], Mod[ 12^(#^2)+1, #^3]==0 &] (* G. C. Greubel, Jan 18 2018 *)
Select[Range[5*10^6], PowerMod[12, #^2, #^3]==#^3-1&] (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Aug 10 2025 *)

Crossrefs

Cf. A127263, A128677, A128678, A128679, A128680, A128681, A128682, A128683, A128684.

Sequence in context: A342811 A301870 A297739 * A292337 A201118 A282968

Adjacent sequences: A128682 A128683 A128684 * A128686 A128687 A128688

Keyword

hard,nonn

Author

Alexander Adamchuk, Mar 31 2007

Extensions

16 more terms from Ryan Propper, Dec 03 2007

Terms a(17) onward from Max Alekseyev, May 14 2010

Status

approved