A226949 Number of twin prime pairs of the form k*n +/- 1 with k <= n.

0, 1, 1, 2, 0, 4, 1, 0, 2, 2, 0, 4, 0, 1, 4, 2, 1, 6, 1, 3, 2, 2, 1, 5, 2, 1, 3, 1, 2, 11, 0, 1, 4, 2, 2, 6, 0, 2, 4, 3, 1, 9, 2, 3, 4, 3, 1, 7, 1, 4, 5, 5, 0, 8, 4, 1, 3, 3, 1, 15, 0, 3, 4, 4, 4, 13, 3, 4, 4, 5, 3, 10, 0, 3, 11, 2, 3, 12, 0, 6, 6, 3, 2, 13, 3

Offset: 1

Author

Irina Gerasimova, Jun 23 2013

Keywords

• nonn

Examples

			a(4) = 2 because there are two twin prime pairs of the form (4k - 1,4k + 1) with 1 <= k <= 4, namely (3, 5) for k = 1 and (11, 13) for k = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014574, A071558.

Programs

Mathematica

a[n_] := Sum[Boole[PrimeQ[k*n - 1] && PrimeQ[k*n + 1]], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Dec 25 2019 *)

PARI

a(n)=sum(k=1,n,isprime(k*n-1)&&isprime(k*n+1)) \\ Charles R Greathouse IV, Jun 27 2013

Extensions

a(7), a(20), a(36) corrected by Charles R Greathouse IV, Jun 27 2013

a(54)-a(90) from Charles R Greathouse IV, Jun 27 2013