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%I #6 Mar 30 2012 17:31:17
%S 4,10,14,24,22,26,36,34,50,52,46,60,58,70,62,80,78,74,84,82,86,94,100,
%T 126,114,106,120,118,130,0,138,0,134,144,142,152,158,162,176,172,166,
%U 0,178,196,0,208,198,194,204,202,230,216,214,236,0,226,0,0,0,0,258,0,254
%N Least even number k such that the Goldbach gap is 2n, or 0 if no such number exists.
%H T. D. Noe, <a href="/A112825/b112825.txt">Table of n, a(n) for n = 0..1000</a>
%e a(1)=10 because the two Goldbach partitions of 10 are {3,7} & {5,5} and (5-3)/2=1.
%t 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]
%Y Cf. A020481.
%K nonn
%O 0,1
%A _Robert G. Wilson v_, Sep 05 2005
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