A112245 Numbers k such that 65537*2^k+1 is prime.

287, 1695, 81359, 512895

Offset

1,1

Comments

Note that 65537=2^16+1 is the largest known Fermat prime. These n yield provable primes. The primes are the smallest numbers in classes 303, 1711 and 81375 of the phi iteration (see A007755).

Jacques Molne found 512895. The corresponding provable prime is the smallest number in class 512911 of the Phi iteration.

Links

Table of n, a(n) for n=1..4.

Prog

(PARI) is(n)=ispseudoprime(65537*2^n+1) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A002253, A002254, A002259, A053345 (F*2^n+1 is prime, where F is a Fermat prime).

Sequence in context: A158252 A236869 A158287 * A289339 A011817 A334008

Adjacent sequences: A112242 A112243 A112244 * A112246 A112247 A112248

Keyword

nonn,hard

Author

T. D. Noe, Aug 30 2005, Aug 26 2007

Status

approved