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A258140
Number of ways to write 6*n + 2 as p^2 + q with p and q both prime.
6
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.
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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 22 2015
STATUS
approved