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, 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, 34, 37, 47, 40, 37, 63, 51, 57, 59, 69, 47, 58, 67, 65, 68, 65, 69, 65, 60, 73, 97, 90, 109, 103, 82, 111, 112, 96, 106, 140
Offset: 1
Keywords
Examples
a(6)=3 because although 13 (the 6th prime) can be expressed as 2*(p1-p2) + 3*p3 in the following ways: 2*(2 - 3) + 3*5 2*(3 - 7) + 3*7 2*(3 - 13) + 3*11 2*(5 - 3) + 3*3 2*(7 - 5) + 3*3 2*(7 - 11) + 3*7 2*(13 - 11) + 3*3 only for the three of them (first, fourth and fifth) p+2*p2 is also a prime (19, 19, 23, respectively).
Programs
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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