A112825 -id:A112825 - cp's OEIS frontend

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

Robert G. Wilson v, Sep 05 2005

nonn

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.

Cf. A020481.

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]

Corrected by T. D. Noe, Feb 14 2011

A112827 Least value k which is the beginning of a null Goldbach chain of length exactly n.

Original entry on oeis.org

60, 184, 242, 114, 2314, 1382

Offset: 1

Robert G. Wilson v, Sep 05 2005

The first even number of A112826(k/2) consisting of a run of n zeros long.

			a(1)=60; a(2)=184 because A112825(92) and A112825(93)=0 but A112825(91) and A112825(94) are not equal to 0.
a(3)=242 because A112825(121), A112825(122) and A112825(123)=0 but A112825(120) and A112825(124) are not equal to 0.

Cf. A020481.

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 + 1]] == 0, t[[a + 1]] = 2n], {n, 2, 10^6}]; g = Flatten[ Position[t, 0]];

cp's OEIS Frontend

A112826 Conjectured values of A112825 which are 0.

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