A257917 a(n) is the largest y 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, 3349888, 33640210518272, 2852314775548000778752, 46730819857678988884581779099803448292025618770199631109363712

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, A257916.

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 2^(2^n) + 1 is composite, then a(n) = A257916(n) - A093179(n).