A112826 Conjectured values of A112825 which are 0.

58, 62, 82, 88, 108, 112, 114, 116, 118, 122, 130, 140, 148, 152, 162, 182, 184, 196, 198, 200, 202, 212, 214, 218, 240, 242, 244, 250, 254, 256, 258, 262, 272, 282, 284, 292, 296, 298, 316, 320, 322, 332, 336, 340, 358, 362, 366, 382, 394, 400, 410, 412

Offset

1,1

Comments

It is conjectured that there does not exist a Goldbach partition yielding a Goldbach "gap" of n as defined, for n=58,62,82,....

These are the even numbers that do not appear in A112824.

Links

Table of n, a(n) for n=1..52.

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];
t = Table[0, {10000}];
Do[a = f[2n]; If[a < 10000 && t[[a/2 + 1]] == 0, t[[a/2 + 1]] = 2n], {n, 2, 10^6}];
Take[ 2*Flatten[ Position[t, 0] - 1], 52]

Crossrefs

Cf. A020481.

Sequence in context: A276186 A346807 A129546 * A224359 A226036 A127024

Adjacent sequences: A112823 A112824 A112825 * A112827 A112828 A112829

Keyword

nonn

Author

Robert G. Wilson v, Sep 05 2005

Extensions

Corrected by T. D. Noe, Feb 14 2011

Status

approved