A217147 Prime numbers after which at least four distinct classes modulo 7 are equally represented among the primes to that point.

2, 3, 5, 7, 11, 13, 17, 139, 181, 199, 211, 223, 227, 823, 1093, 1373, 2713, 2741, 2753, 9041, 9619, 9623, 9743, 9749, 21467, 21503, 21529, 260017, 6399433, 59998271, 1404351607

Offset

1,1

Comments

Only after 13 and 223 are five of the congruence classes modulo 7 equally represented, and it's not unreasonable to conjecture that this holds permanently.

Links

Table of n, a(n) for n=1..31.

Example

At the 31st term, 1404351607, 11698330 primes have occurred congruent to each of 1, 2, 3 and 4 modulo 7.

Mathematica

t = {}; mdCnt = {0, 0, 0, 0, 0, 0, 0}; Do[p = Prime[i]; mdCnt[[Mod[p, 7] + 1]]++; ty = Tally[mdCnt]; If[Select[ty, #[[2]] >= 4 &] != {}, AppendTo[t, p]], {i, 100000}]; t (* T. D. Noe, Sep 27 2012 *)

Crossrefs

Sequence in context: A241716 A061166 A003681 * A029732 A037950 A330224

Adjacent sequences: A217144 A217145 A217146 * A217148 A217149 A217150

Keyword

nonn

Author

James G. Merickel, Sep 27 2012

Status

approved