A055626 First prime starting a chain of exactly n consecutive primes congruent to 5 modulo 6.

5, 23, 47, 251, 1889, 7793, 43451, 243161, 726893, 759821, 2280857, 1820111, 10141499, 40727657, 19725473, 136209239, 744771077, 400414121, 1057859471, 489144599, 13160911739, 766319189, 38451670931, 119618704427, 21549657539, 141116164769, 140432294381, 437339303279

Offset

1,1

Comments

The term "exactly" means that before the first and after the last primes of chain, the immediate primes are not congruent to 5 modulo 6.

a(21)>2^31, a(22)= 766319189. - Hugo Pfoertner, Jul 31 2003

See A057622 for the variant where "exactly" is replaced by "at least". See A055625 for the variant "congruent to 1 (mod 6)". - M. F. Hasler, Sep 03 2016

Links

Giovanni Resta, Table of n, a(n) for n = 1..35 (terms < 4*10^14)

J. K. Andersen, Consecutive Congruent Primes.

Mathematica

pp = Table[{p = Prime[n], Mod[p, 6]}, {n, 10^6}];
sp = Split[pp, Mod[#1[[2]], 6] == Mod[#2[[2]], 6]&];
a[n_] := SelectFirst[sp, Length[#] == n && MatchQ[#, {{_Integer, 5} ..}]& ][[1, 1]];
Table[an = a[n]; Print[n, " ", an]; an, {n, 1, 13}] (* Jean-François Alcover, Nov 21 2018 *)

Prog

See link in A085516.
(PARI) okchain(n, p) = {if ((precprime(p-1) % 6) == 5, return (0)); for (i=1, n, if ((p % 6) != 5, return (0)); p = nextprime(p+1); ); if ((p % 6) == 5, 0, 1); }
a(n) = {p = 5; while (! okchain(n, p), p = nextprime(p+1)); p; } \\ Michel Marcus, Dec 17 2013

Crossrefs

Cf. A055623, A055624, A055625, A085516.

Sequence in context: A107011 A031387 A057622 * A127200 A147113 A135771

Adjacent sequences: A055623 A055624 A055625 * A055627 A055628 A055629

Keyword

nonn

Author

Labos Elemer, Jun 05 2000

Extensions

a(9)-a(13), including correction of a(9)-a(10) from Reiner Martin, Jul 18 2001

a(14)-a(20) from Hugo Pfoertner, Jul 31 2003

a(21)-a(25) from Jens Kruse Andersen, May 30 2006

a(26) and beyond from Giovanni Resta, Aug 04 2013

Status

approved