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A257916
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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.
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2
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OFFSET
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0,6
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COMMENTS
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2^(2^n) + 1 belongs to A019434 if and only if a(n) = 0.
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REFERENCES
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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.
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LINKS
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FORMULA
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If F(n) = 2^(2^n) + 1 is composite, then a(n) = (A032742(F(n)) + A093179(n))/2.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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