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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 (list; graph; refs; listen; history; text; internal format)
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, Pgs 441-446, 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}] (from 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

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Last modified December 18 17:15 EST 2014. Contains 252173 sequences.