A234955 Trisection of A107926: The least number k such that there are primes p and q with p - q = 6*n+2, p + q = k, and p the least such prime >= k/2.

8, 54, 108, 234, 228, 414, 516, 1182, 612, 1038, 1776, 1074, 3312, 1398, 1728, 2706, 2844, 4902, 1152, 3870, 2724, 4974, 2328, 6222, 5040, 13194, 10236, 5838, 8952, 9642, 9816, 12906, 21900, 11958, 14712, 6294, 15984, 9498, 31752, 31602, 6096, 37854, 41208, 6114

Offset: 1

Author

Robert G. Wilson v, Jan 01 2014

Keywords

• nonn

Comments

All terms found to date are congruent to 0 (mod 6), except for a(1).

Record values: 8, 54, 108, 228, 414, 516, 612, 1038, 1074, 1152, 2328, 5040, 5838, 6096, 6114, 22194, 37764, 37902, 99432, 136116, 176856, 318144, 410712, 1079952, 1436448, 2549346, 3278118, 7012944, 8268534, 11283126, 11284134, 22614234, 37510062, 41607234, 94089894, 139419954, 144049014, 305966316, 378180246, 490373322, 998189838, 1326486408, 1373334486, 1445744268, 2016602694, 2247482688, 3239350182, 3884888976, 5147119596, 7172019282, …, .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..867

Crossrefs

Cf. A107926, A231156, A234956.

Programs

Mathematica

f[n_] := Block[{p = n/2}, While[ !PrimeQ[n - p], p = NextPrime@ p]; p - n/2]; t = Table[0, {10000}]; k = 4;  While[k < 12475000001, If[ t[[f@ k]] == 0, t[[f@ k]] = k; Print[{f@ k, k}]]; k += 2]; Table[ t[[n]], {n, 2, 5000, 3}]

Formula

a(n) = A107926(3n-2).