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

Author

Alexander Adamchuk, Mar 31 2007

Keywords

• hard
• nonn

Comments

13 divides a(n) for n > 1.

Crossrefs

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

Programs

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 *)

Extensions

16 more terms from Ryan Propper, Dec 03 2007

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