A258140 Number of ways to write 6*n + 2 as p^2 + q with p and q both prime.

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

Offset

0,6

Comments

Conjecture: a(n) > 0 except for n = 0, 1, 12, 28, 102, 117, 168, 4079.

See also the comments in A258139.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 0..10000

Example

a(5) = 2 since 6*5 + 2 = 3^2 + 23 = 5^2 + 7 with 3, 23, 5, 7 all prime.

Mathematica

Do[r=0; Do[If[PrimeQ[6n+2-Prime[k]^2], r=r+1], {k, 1, PrimePi[Sqrt[6n+2]]}]; Print[n, " ", r]; Continue, {n, 0, 100}]

Prog

(PARI) a(n)=my(t=6*n+2, s); forprime(p=2, sqrtint(t-2), if(isprime(t-p^2), s++)); s \\ Charles R Greathouse IV, May 26 2015

Crossrefs

Cf. A000040, A002375, A258139, A258141.

Sequence in context: A110659 A308068 A100522 * A140408 A047080 A036064

Adjacent sequences: A258137 A258138 A258139 * A258141 A258142 A258143

Keyword

nonn

Author

Zhi-Wei Sun, May 22 2015

Status

approved