%I
%S 0,0,0,1,0,3,7,5,7,8,6,17,15,10,13,19,9,21,24,18,29,28,25,37,37,29,32,
%T 34,37,47,40,37,63,51,57,59,69,47,58,67,65,68,65,69,65,60,73,97,90,
%U 109,103,82,111,112,96,106,140
%N Number of representations of prime p = prime(n) as 2*(p1p2)+3*p3 (where p1, p2, p3 are primes less than or equal to p), for which p+2*p2(=2*p1+3*p3) is also a prime.
%e a(6)=3 because although 13 (the 6th prime) can be expressed as 2*(p1p2) + 3*p3 in the following ways:
%e 2*(2  3) + 3*5
%e 2*(3  7) + 3*7
%e 2*(3  13) + 3*11
%e 2*(5  3) + 3*3
%e 2*(7  5) + 3*3
%e 2*(7  11) + 3*7
%e 2*(13  11) + 3*3
%e only for the three of them (first, fourth and fifth) p+2*p2 is also a prime (19, 19, 23, respectively).
%o (PARI) a(n) = {my(vp = primes(n), nb=0, p=prime(n), p1, p2, p3); for (i=1, #vp, p1 = vp[i]; for (j=1, #vp, p2 = vp[j]; for (k=1, #vp, p3 = vp[k]; if ((2*(p1p2) + 3*p3 == p) && isprime(p+2*p2), nb++);););); nb;} \\ _Michel Marcus_, Jan 26 2021
%Y Cf. A120450, A120451.
%K nonn
%O 1,6
%A _Vassilis Papadimitriou_, Sep 11 2006
