A306995 Number of primes q < prime(n), such that 2*prime(n) + q is prime.

0, 0, 1, 2, 1, 3, 3, 2, 2, 2, 3, 3, 3, 5, 6, 4, 3, 5, 7, 3, 6, 5, 6, 6, 7, 5, 5, 8, 6, 7, 8, 5, 9, 9, 4, 8, 8, 12, 8, 10, 8, 9, 11, 10, 10, 10, 8, 10, 12, 9, 10, 10, 11, 11, 9, 10, 11, 13, 15, 11, 12, 13, 14, 11, 16, 15, 11, 13, 10, 15, 14, 12, 13, 16, 16, 13, 17, 15, 15

Offset

1,4

Comments

Conjecture: a(n) > 0 for all n >= 3. - Dmitry Kamenetsky, Mar 18 2019

Links

Table of n, a(n) for n=1..79.

Formula

a(n) = A071127(prime(n)). - Michel Marcus, Mar 19 2019

Example

2*7 + 3 = 17 and 2*7 + 5 = 19 are prime. Hence a(4) = 2.

Prog

(PARI) a(n) = my(s=0, p=prime(n)); forprime(i=1, p-1, s += isprime(2*p+i)); s; \\ Michel Marcus, Mar 19 2019

Crossrefs

Cf. A071127, A306996, A306997.

Sequence in context: A337137 A035050 A198790 * A212907 A308584 A046819

Adjacent sequences: A306992 A306993 A306994 * A306996 A306997 A306998

Keyword

nonn

Author

Dmitry Kamenetsky, Mar 18 2019

Status

approved