A224965 Let p = prime(n). a(n) = number of primes q less than p, such that both p*q+p+q and p*q-p-q are primes.

0, 0, 2, 3, 1, 2, 2, 2, 1, 2, 1, 1, 3, 2, 1, 1, 1, 3, 2, 2, 1, 3, 1, 0, 4, 0, 1, 2, 5, 0, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 4, 2, 1, 0, 2, 5, 1, 1, 3, 1, 3, 3, 3, 0, 1, 2, 4, 1, 4, 4, 2, 2, 2, 6, 2, 5, 2, 3, 3, 2, 4, 5, 3, 2, 1, 3, 1, 3, 3, 3, 2, 2, 3, 2

Offset

1,3

Links

Table of n, a(n) for n=1..85.

Example

For n=3, p=5, there are a(3)=2 solutions 2,3 since 5*2+5+2=17, 5*2-5-2=3 and 5*3+5+3=23, 5*3-5-3=7. Also for n=5, p=11, there is a(5)=1 solution in the form of 11*3+11+3=47, 11*3-11-3=19.

Mathematica

Table[p = Prime[n]; c = 0; i = 1; While[i < n, q1 = p*Prime[i]; q2 = p + Prime[i]; If[PrimeQ[q1 + q2] && PrimeQ[q1 - q2], c = c + 1]; i++]; c, {n, 85}]

Crossrefs

Cf. A224748, A224908, A224925, A224962.

Sequence in context: A128864 A106798 A214640 * A194298 A194306 A283325

Adjacent sequences: A224962 A224963 A224964 * A224966 A224967 A224968

Keyword

nonn

Author

Jayanta Basu, Apr 21 2013

Status

approved