A282194 a(n) = smallest positive k such that 2*n + 2^k + 1 is composite.

3, 5, 2, 1, 4, 2, 1, 7, 2, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 4, 2, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 4, 2, 1, 4, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1

Offset: 0

Author

Altug Alkan, Feb 15 2017

Keywords

• nonn

Comments

Least k such that a(k) = n are 3, 2, 0, 4, 1, 112, 7, 32917, 802, 9712, 1198673602 for the initial terms.

Examples

			a(1) = 5 because 3 + 2^k is prime for 0 < k < 5 and 3 + 2^5 = 35 is composite.
		

Links

• Altug Alkan, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A067076, A067760, A153238, A282026.

Programs

Mathematica

spk[n_]:=Module[{k=1},While[!CompositeQ[2n+2^k+1],k++];k]; Array[spk,110,0] (* Harvey P. Dale, Apr 26 2017 *)

PARI

a(n) = my(k=1); while(isprime(2*n+2^k+1), k++); k;