A280667 a(n) = number of primes of the form 4k + 1 such that 2n - 4k - 1 is prime.

0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 4, 0, 3, 4, 3, 4, 5, 2, 3, 4, 3, 5, 6, 0, 5, 6, 2, 4, 6, 3, 5, 6, 4, 3, 8, 2, 4, 6, 4, 4, 7, 2, 6, 8, 5, 5, 8, 4, 7, 10, 6, 6, 12, 3, 5, 10, 3, 6, 9, 4, 5, 6, 7, 8, 11, 3, 5, 10, 4, 8, 11, 2, 8, 10, 5, 6, 13, 6, 6, 8, 7, 7, 14, 2, 8, 12, 5

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 07 2017

Keywords

• nonn

Comments

Primes p such that a(p) = 0: 2, 3, 7, 19, 31.

Examples

			a(8) = 2 because 2*8 - 4*1 - 1 = 11 is prime where 4*1 + 1 = 5 is prime of the form 4k+1 and 2*8 - 4*3 - 1 = 3 is prime where 4*3 + 1 = 13 is prime of the form 4k+1.
		

Crossrefs

Cf. A002144, A035026, A278287, A279027.

Programs

Magma

A280667 := func; [A280667(n):n in[1..100]];

PARI

a(n) = sum(k=1, 2*n, isprime(k) && isprime(2*n-k) && ((2*n-k) % 4 == 1)); \\ Michel Marcus, Jan 07 2017