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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.

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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, 24, 22, 28, 20, 24, 24, 26, 26, 34, 26, 32, 30, 38, 36, 40, 36, 36, 28, 42, 36, 18, 44, 38, 40, 50, 42, 40, 50, 48, 40, 54, 52, 48, 42, 46, 42, 56, 56, 64, 48, 60, 64, 68, 66, 66, 48, 60 (list; graph; listen)

	OFFSET	`2,4`
	COMMENT	`The gap is always even.`
	FORMULA	`A112823 - A020481.`
	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]; Table[ f[n], {n, 4, 150, 2}]`
	CROSSREFS	`Cf. A020481.` `Sequence in context: A144289 A037035 A159984 this_sequence A001100 A136265 A066910` `Adjacent sequences: A112821 A112822 A112823 this_sequence A112825 A112826 A112827`
	KEYWORD	`nonn`
	AUTHOR	`Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 05 2005`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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