A112825 Least even number k such that the Goldbach gap is 2n, or 0 if no such number exists.

4, 10, 14, 24, 22, 26, 36, 34, 50, 52, 46, 60, 58, 70, 62, 80, 78, 74, 84, 82, 86, 94, 100, 126, 114, 106, 120, 118, 130, 0, 138, 0, 134, 144, 142, 152, 158, 162, 176, 172, 166, 0, 178, 196, 0, 208, 198, 194, 204, 202, 230, 216, 214, 236, 0, 226, 0, 0, 0, 0, 258, 0, 254

Offset: 0

Author

Robert G. Wilson v, Sep 05 2005

Keywords

• nonn

Examples

			a(1)=10 because the two Goldbach partitions of 10 are {3,7} & {5,5} and (5-3)/2=1.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A020481.

Programs

Mathematica

f[n_] := Block[{p = 2, q = n/2}, While[ !PrimeQ[p] || !PrimeQ[n - p], p++ ]; While[ !PrimeQ[q] || !PrimeQ[n - q], q-- ]; q - p]; t = Table[0, {100}]; Do[a = f[2n]; If[a < 100 && t[[a/2 + 1]] == 0, t[[a/2 + 1]] = 2n; Print[{2a, 2n}]], {n, 2, 10^4}]; Take[t, 63]