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.

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

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