A309265 Numbers k such that s + t = k with 0 < s < t where s and t-s are both prime.

6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 31, 33, 35, 36, 37, 39, 40, 41, 43, 45, 47, 48, 49, 51, 53, 55, 57, 59, 60, 61, 63, 64, 65, 67, 69, 71, 73, 75, 76, 77, 79, 81, 83, 84, 85, 87, 88, 89, 91, 93, 95, 96, 97, 99, 101, 103, 105

Offset: 1

Author

Wesley Ivan Hurt, Jul 19 2019

Keywords

• nonn

Comments

Essentially the same as A210147 with s=p, t-s=q. - R. J. Mathar, Aug 09 2019

Examples

			6 is in the sequence since there are numbers s=2 and t=4 such that s + t = 6 with s < t, and where s=2 and t-s = 4-2 = 2 are both prime.
7 is in the sequence since there are numbers s=3 and t=5 such that s + t = 7 with s < t and where s=3 and t-s = 5-3 = 2 are both prime.
		

Crossrefs

Cf. A309152, A309264.

Programs

Mathematica

Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - 2 i] - PrimePi[n - 2 i - 1]), {i, Floor[n/2]}] > 0, n, {}], {n, 100}]]

PARI

isok(k) = {forprime (s=1, k, if (((t = k - s) > s) && isprime(t-s), return (1)););} \\ Michel Marcus, Jul 20 2019