A094499 Smallest prime factor of 2^(2^n)+3^(2^n), i.e., exponents are powers of 2.

13, 97, 17, 3041, 1153, 769, 257, 72222721, 4043777, 2330249132033, 625483777, 286721, 14496395542529, 2752513, 65537, 319291393, 54498164737

Offset: 1

Author

Labos Elemer, Jun 02 2004

Keywords

• nonn

Comments

Factors are of the form k*2^(n+1)+1.

Links

• Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
• Anders Björn and Hans Riesel, Factors of generalized Fermat numbers, Math. Comp. 67 (1998), no. 221, pp. 441-446.

Crossrefs

Cf. A050244, A294132.

Programs

Mathematica

f[n_] := Block[{k = 1, m = 2^(n + 1)}, While[ Mod[ PowerMod[2, 2^n, k*m + 1] + PowerMod[3, 2^n, k*m + 1], k*m + 1] != 0, k++ ]; k*m + 1]; Table[ f[n], {n, 9}] (* Robert G. Wilson v, Jun 03 2004 *)

Extensions

Edited and extended by Robert G. Wilson v, Jun 03 2004