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A122001 Number of representations of prime p = prime(n) as 2*(p1-p2)+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. 0

%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*(p1-p2)+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*(p1-p2) + 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*(p1-p2) + 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

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Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)