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%I #17 Jun 08 2015 05:07:59
%S 0,0,0,0,0,3350529,33640210792449,2852374425137128275969,
%T 46730819857678988884581779099803448292025618771438557470916609
%N a(n) is the largest x that is a member of a pair (x, y) of integers with x - y > 1 such that x^2 - y^2 is equal to the Fermat number 2^(2^n) + 1, or 0 if no such number exists.
%C 2^(2^n) + 1 belongs to A019434 if and only if a(n) = 0.
%D M. Krizek, F. Luca, L. Somer, 17 Lectures on Fermat Numbers: From Number Theory to Geometry, CMS Books in Mathematics, vol. 9, Springer-Verlag, New York, 2001, p. 6.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fermat_number">Fermat number</a>
%F If F(n) = 2^(2^n) + 1 is composite, then a(n) = (A032742(F(n)) + A093179(n))/2.
%o (PARI) a(n) = {my(fn = 2^(2^n) + 1); if (isprime(fn), return (0)); my(spf = factor(fn)[1,1]); (fn/spf + spf)/2;} \\ _Michel Marcus_, Jun 07 2015
%Y Cf. A000215, A257917.
%K nonn
%O 0,6
%A _Arkadiusz Wesolowski_, May 12 2015
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