

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
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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



