A260821 Least positive integer k for which n*2^(2^k) + 1 is composite.

5, 1, 2, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 3, 1, 2, 3, 1, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 5, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 2

Offset: 1

Author

Marco Ripà, Jul 31 2015

Keywords

• nonn

Comments

a(n) = 1 for nonzero n in A045751. - Michel Marcus, Aug 01 2015

Examples

			a(7)=3 because 7*2^2 + 1 = 29 is prime and 7*2^(2^2) + 1 = 113 is also prime, while 7*2^(2^3) + 1 = 11*163.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045751, A005098.

Programs

Mathematica

A260821[n_] := Module[{k = 0}, While[PrimeQ[n*2^(2^++k) + 1]]; k];
Array[A260821, 100] (* Paolo Xausa, Jan 31 2024 *)

PARI

a(n) = {k = 1; while (isprime(n*2^2^k+1), k++); k;} \\ Michel Marcus, Aug 01 2015

Extensions

More terms from Michel Marcus, Aug 01 2015