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%I #22 Jul 08 2023 15:18:13
%S 13,97,17,3041,1153,769,257,72222721,4043777,2330249132033,625483777,
%T 286721,14496395542529,2752513,65537,319291393,54498164737
%N Smallest prime factor of 2^(2^n)+3^(2^n), i.e., exponents are powers of 2.
%C Factors are of the form k*2^(n+1)+1.
%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.
%H Anders Björn and Hans Riesel, <a href="https://doi.org/10.1090/S0025-5718-98-00891-6">Factors of generalized Fermat numbers</a>, Math. Comp. 67 (1998), no. 221, pp. 441-446.
%t 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 *)
%Y Cf. A050244, A294132.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 02 2004
%E Edited and extended by _Robert G. Wilson v_, Jun 03 2004
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