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%I #12 May 26 2015 10:59:26
%S 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,
%T 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,
%U 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
%N Number of ways to write 6*n + 2 as p^2 + q with p and q both prime.
%C Conjecture: a(n) > 0 except for n = 0, 1, 12, 28, 102, 117, 168, 4079.
%C See also the comments in A258139.
%H Zhi-Wei Sun, <a href="/A258140/b258140.txt">Table of n, a(n) for n = 0..10000</a>
%e a(5) = 2 since 6*5 + 2 = 3^2 + 23 = 5^2 + 7 with 3, 23, 5, 7 all prime.
%t 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}]
%o (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
%Y Cf. A000040, A002375, A258139, A258141.
%K nonn
%O 0,6
%A _Zhi-Wei Sun_, May 22 2015
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