

A094499


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


2



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

1,1


COMMENTS

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


REFERENCES

Anders Bjorn and Hans Riesel, Factors of Generalized Fermat Numbers, Mathematics of Computation, Vol. 67, Nbr 221, pp. 441446, 1998.


LINKS

Table of n, a(n) for n=1..17.
Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
Anders Bjorn and Hans Riesel, Factors of Generalized Fermat numbers..


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 *)


CROSSREFS

Sequence in context: A044645 A153703 A222503 * A242385 A141894 A160554
Adjacent sequences: A094496 A094497 A094498 * A094500 A094501 A094502


KEYWORD

nonn


AUTHOR

Labos Elemer, Jun 02 2004


EXTENSIONS

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


STATUS

approved



