

A217147


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


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



