A309264 Numbers k such that s + t = k with 0 < s < t where t and t - s are both prime.

4, 7, 8, 9, 11, 12, 15, 17, 19, 20, 21, 23, 24, 25, 27, 29, 31, 32, 33, 35, 36, 39, 41, 43, 44, 45, 47, 49, 51, 53, 55, 56, 57, 59, 60, 61, 63, 65, 67, 69, 71, 72, 73, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 91, 92, 93, 95, 97, 99, 101, 103, 104, 105, 107

Offset

1,1

Links

Table of n, a(n) for n=1..64.

Example

4 is in the sequence since there are numbers, s=1 and t=3, that satisfy s + t = 4, where s < t, t = 3 (prime) and t - s = 3 - 1 = 2 (prime).
7 is in the sequence since there are numbers, s=2 and t=5 that satisfy s + t = 7, where s < t, t = 5 (prime) and t - s = 5 - 2 = 3 (prime).

Mathematica

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

Prog

(PARI) isok(k) = {forprime (t=1, k, if (((s = k - t) < t) && (s > 0) && isprime(t-s), return (1)); ); } \\ Michel Marcus, Jul 20 2019

Crossrefs

Cf. A309152, A309265.

Sequence in context: A004710 A060257 A262874 * A161986 A324940 A020670

Adjacent sequences: A309261 A309262 A309263 * A309265 A309266 A309267

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 19 2019

Status

approved