A066285 a(n) is the minimal difference between primes p and q whose sum is 2n.

0, 0, 2, 0, 2, 0, 6, 4, 6, 0, 2, 0, 6, 4, 6, 0, 2, 0, 6, 4, 18, 0, 10, 12, 6, 8, 18, 0, 2, 0, 18, 8, 6, 12, 10, 0, 18, 4, 6, 0, 2, 0, 6, 4, 30, 0, 10, 24, 6, 16, 18, 0, 14, 24, 6, 8, 30, 0, 2, 0, 18, 8, 6, 12, 10, 0, 30, 4, 6, 0, 2, 0, 30, 8, 6, 12, 10, 0, 18, 4, 30, 0, 10, 24, 6, 28, 18, 0

Offset: 2

Author

Dean Hickerson, Dec 12 2001

Keywords

• nonn
• easy

Comments

Terms are always even numbers because primes present in Goldbach partitions of n > 4 are odd and n = 4 has just one partition (2+2) where the difference is 0. a(n) = 0 iff n is prime. - Marcin Barylski, Apr 28 2018

Crossrefs

Cf. A002372, A047160, A065978, A066286, A303603.

Programs

Mathematica

a[n_] := For[p=n, True, p--, If[PrimeQ[p]&&PrimeQ[2n-p], Return[2n-2p]]]

PARI

a(n) = {forstep(k=n, 1, -1, if (isprime(k) && isprime(2*n-k), return(2*n-2*k)););} \\ Michel Marcus, Jun 01 2020

Formula

a(n) = 2 * A047160(n). - Alois P. Heinz, Jun 01 2020