A361546 a(n) is the least odd number k such that k*2^prime(n) + 1 is prime, or -1 if no such number k exists.

1, 5, 3, 5, 9, 5, 9, 11, 45, 23, 35, 15, 3, 9, 27, 51, 27, 53, 9, 39, 23, 249, 51, 51, 131, 221, 29, 105, 321, 179, 5, 221, 111, 411, 191, 65, 83, 75, 95, 101, 147, 83, 149, 111, 203, 131, 9, 245, 281, 15, 83, 65, 299, 39, 51, 51, 225, 65, 81, 125, 611, 143, 65, 107, 21

Offset: 1

Author

Jean-Marc Rebert, Mar 15 2023

Keywords

• nonn

Examples

			prime(1) = 2 and 1*2^2 + 1 = 5 is prime, and no lesser odd k satisfies this, so a(1) = 1.
		

Links

• Jean-Marc Rebert, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A076336. Essentially the same as A253398.

Programs

Mathematica

a[n_] := Module[{m = 2^Prime[n], k = 1}, While[!PrimeQ[k*m + 1], k += 2]; k]; Array[a, 65] (* Amiram Eldar, Mar 15 2023 *)

PARI

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