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

Author

Robert G. Wilson v, Sep 05 2005

Keywords

• nonn

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.

Crossrefs

Cf. A020481.

Programs

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]

Extensions

Corrected by T. D. Noe, Feb 14 2011