A206038 - OEIS

A206038

Values of the difference d for 4 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 3.

6, 12, 18, 42, 48, 54, 84, 96, 126, 132, 252, 348, 396, 426, 438, 474, 594, 636, 642, 648, 678, 804, 858, 1176, 1218, 1272, 1302, 1314, 1362, 1428, 1482, 1566, 1692, 1728, 1896, 1992, 2064, 2106, 2238, 2394, 2442, 2574, 2616, 2688, 2694, 2706, 2832, 2856, 2898

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OFFSET

1,1

COMMENTS

The computations were done without any assumptions on the form of d.

LINKS

Sameen Ahmed Khan, Table of n, a(n) for n = 1..10000

S. A. Khan, Primes in Geometric-Arithmetic Progression, arXiv preprint arXiv:1203.2083, 2012. - From N. J. A. Sloane, Sep 15 2012

EXAMPLE

d = 18 then {5, 5 + 1*18, 5 + 2*18, 5 + 3*18} = {5, 23, 41, 59}, which is 4 primes in arithmetic progression.

MATHEMATICA

t={}; Do[If[PrimeQ[{5, 5 + d, 5 + 2*d, 5 + 3*d}] == {True, True, True, True}, AppendTo[t, d]], {d, 3000}]; t