A280134 Number of primes of the form 4(n - k - 1) + 3 where 0 <= k and prime of the form 4k + 3 <= n.

0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 1, 4, 3, 1, 4, 3, 2, 3, 4, 3, 2, 5, 3, 2, 4, 2, 4, 4, 3, 4, 4, 3, 3, 5, 2, 2, 6, 4, 2, 5, 4, 3, 6, 3, 2, 3, 4, 4, 5, 3, 2, 6, 4, 3, 5, 1, 5, 6, 2, 3, 4, 4, 3, 6, 3, 4, 8, 3, 3, 4, 3, 3, 5, 2, 2, 6, 4, 3, 6, 5

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 26 2016

Keywords

• nonn

Comments

(1) Conjecture: a(n) > 0 for n >= 11.

(2) Conjecture: A278287(n) > 0 for n >= 11.

Conjecture (1) and conjecture (2) are first and second parts of Goldbach-like conjecture in A001031.

Examples

			a(12) = 2 because 4*(12-0-1)+3 = 47 and 4*0+3 = 3 are primes where 3 < 12 and 4*(12-1-1)+3 = 43 and 4*1+3 = 7 are primes where 7 < 12.
		

Crossrefs

Cf. A001031, A002144, A278287.