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

1,1

Comments

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

Links

Table of n, a(n) for n=1..65.

Example

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.

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}]]

Prog

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

Crossrefs

Cf. A309152, A309264.

Sequence in context: A081408 A143616 A005050 * A309404 A120191 A059983

Adjacent sequences: A309262 A309263 A309264 * A309266 A309267 A309268

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 19 2019

Status

approved