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
Keywords
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.
Programs
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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
Comments