A037039 Least k such that 4*n*k+1 is a prime.

1, 2, 1, 1, 2, 3, 1, 3, 1, 1, 2, 2, 1, 2, 1, 3, 2, 1, 3, 3, 4, 1, 3, 1, 1, 3, 1, 1, 2, 2, 3, 2, 3, 1, 2, 3, 1, 3, 1, 4, 5, 2, 1, 2, 1, 7, 5, 1, 1, 2, 2, 6, 5, 2, 3, 2, 1, 1, 3, 1, 3, 6, 3, 1, 2, 5, 1, 5, 1, 1, 2, 2, 1, 2, 2, 4, 2, 1, 1, 2, 4, 7, 3, 1, 3, 3, 1, 1, 3, 5, 3, 9, 1, 3, 2, 2, 1, 8, 1, 1, 2, 1, 3, 3, 1

Offset: 1

Author

Felice Russo

Keywords

• nonn

Examples

			a(5)=2 because for n=5: 4*5*2+1=41 is a prime.
		

Crossrefs

Cf. A016014.

Programs

Mathematica

Table[Module[{k=1},While[!PrimeQ[4 n*k+1],k++];k],{n,110}] (* Harvey P. Dale, Aug 11 2025 *)

PARI

a(n) = my(k = 0); while (! isprime(4*n*k+1), k++); k; \\ Michel Marcus, Sep 28 2013

Extensions

More terms from Erich Friedman