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A112824 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. 2
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; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

The gap is always even.

LINKS

T. D. Noe, Table of n, a(n) for n = 2..1000

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: A159984 A240697 A271230 * A195133 A308022 A001100

Adjacent sequences:  A112821 A112822 A112823 * A112825 A112826 A112827

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Sep 05 2005

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)