

A066285


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


6



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
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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[2np], Return[2n2p]]]


PROG

(PARI) a(n) = {forstep(k=n, 1, 1, if (isprime(k) && isprime(2*nk), return(2*n2*k)); ); } \\ Michel Marcus, Jun 01 2020


CROSSREFS

Cf. A002372, A047160, A065978, A066286, A303603.
Sequence in context: A136581 A175950 A339423 * A327873 A136665 A047765
Adjacent sequences: A066282 A066283 A066284 * A066286 A066287 A066288


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson, Dec 12 2001


STATUS

approved



