A257916 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.

0, 0, 0, 0, 0, 3350529, 33640210792449, 2852374425137128275969, 46730819857678988884581779099803448292025618771438557470916609

Offset: 0

Author

Arkadiusz Wesolowski, May 12 2015

Keywords

• nonn

Comments

2^(2^n) + 1 belongs to A019434 if and only if a(n) = 0.

References

• 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.

Links

• Wikipedia, Fermat number

Crossrefs

Cf. A000215, A257917.

Programs

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

Formula

If F(n) = 2^(2^n) + 1 is composite, then a(n) = (A032742(F(n)) + A093179(n))/2.