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

Author

Zhi-Wei Sun, May 22 2015

Keywords

• nonn

Comments

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

See also the comments in A258139.

Examples

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

Links

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

Crossrefs

Cf. A000040, A002375, A258139, A258141.

Programs

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}]

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