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

2,3

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

Links

Table of n, a(n) for n=2..89.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A354607 A175950 A339423 * A327873 A136665 A047765

Adjacent sequences: A066282 A066283 A066284 * A066286 A066287 A066288

Keyword

nonn,easy

Author

Dean Hickerson, Dec 12 2001

Status

approved