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%I #4 Mar 30 2012 17:31:17
%S 0,0,0,2,0,4,2,2,4,8,6,10,6,6,10,14,12,12,14,14,10,20,14,16,18,16,16,
%T 24,22,28,20,24,24,26,26,34,26,32,30,38,36,40,36,36,28,42,36,18,44,38,
%U 40,50,42,40,50,48,40,54,52,48,42,46,42,56,56,64,48,60,64,68,66,66,48,60
%N Consider the Goldbach conjecture that every even number 2n=p+p' with p<=p'. Consider all such Goldbach partitions; a(n) is the difference between the largest p and the smallest p. Call this difference the Goldbach gap.
%C The gap is always even.
%H T. D. Noe, <a href="/A112824/b112824.txt">Table of n, a(n) for n = 2..1000</a>
%F A112823 - A020481.
%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]; Table[ f[n], {n, 4, 150, 2}]
%Y Cf. A020481.
%K nonn
%O 2,4
%A _Robert G. Wilson v_, Sep 05 2005
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