A056898 a(n) = smallest number m such that m^2+n is prime.

1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 4, 1, 0, 7, 2, 9, 2, 1, 0, 1, 0, 3, 2, 3, 6, 1, 0, 3, 2, 1, 0, 1, 0, 3, 4, 1, 0, 5, 2, 3, 4, 1, 0, 5, 2, 9, 2, 1, 0, 1, 0, 3, 2, 3, 6, 1, 0, 9, 2, 1, 0, 1, 0, 3, 2, 5, 6, 1, 0, 3, 4, 1, 0, 5, 2, 9, 4, 1, 0, 7, 4, 3, 2, 3, 6, 1, 0, 3, 2

Offset: 1

Author

Henry Bottomley, Jul 05 2000

Keywords

• nonn

Examples

			a(8) = 3 since 3^2+8 = 17 which is prime.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000040, A002496, A056892, A056893, A056894, A056895, A056896, A056897.

Programs

PARI

A056898(n) = { my(m=0); while(!isprime((m*m)+n),m++); (m); }; \\ Antti Karttunen, Mar 04 2018

Formula

a(n) = sqrt(A056896(n)-n) = sqrt(A056897(n)).

For p a prime: a(p) = 0 (and a(p-1) = 1 if p<>3).