A377842 a(n) = q - 2*p, where q is the greatest prime such that p=2*n - q is also prime.

-2, -3, -1, 1, -3, 5, 7, 3, 11, 13, 9, 17, 13, 9, 23, 25, 21, 17, 31, 27, 35, 37, 33, 41, 37, 33, 47, 43, 39, 53, 55, 51, 47, 61, 57, 65, 67, 63, 59, 73, 69, 77, 73, 69, 83, 79, 75, 41, 91, 87, 95, 97, 93, 101, 103, 99, 107, 103, 99, 83, 91, 87, 71, 121, 117, 125, 121, 117, 131, 133

Offset: 2

Author

Michel Eduardo Beleza Yamagishi, Dec 10 2024

Keywords

• sign

Links

• M. E. B. Yamagishi, Goldbach's Conjecture: A Simple and Fast Algorithm, Preprint, 2024.

Crossrefs

Cf. A020481, A020482, A378896.

Programs

Mathematica

Table[Module[{p = 2, q},
  While[True, q = 2 n - p; If[PrimeQ[p] && PrimeQ[q], Break[]];
   p = NextPrime[p]]; q - 2 p], {n, 2, 100}]

PARI

a(n) = my(q=precprime(2*n)); while (!isprime(2*n - q), q = precprime(q-1)); q - 2*(2*n-q); \\ Michel Marcus, Dec 12 2024