A055625 First prime starting a chain of exactly n consecutive primes congruent to 1 modulo 6.

7, 31, 151, 3049, 7351, 1741, 19471, 118801, 498259, 148531, 406951, 2513803, 2339041, 89089369, 51662593, 73451737, 232301497, 450988159, 1558562197, 2506152301, 1444257673, 28265029657, 24061965043, 87996684091, 43553959717

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 1 modulo 6.

See A057620 for the variant where "exactly" is replaced by "at least". - 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.

A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

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, 1} ..}]& ][[1, 1]];
Table[an = a[n]; Print[n, " ", an]; an, {n, 1, 13}] (* Jean-François Alcover, Nov 21 2018 *)

Prog

See link in A085515.

Crossrefs

Cf. A055623, A055624, A055626, A085515.

Sequence in context: A121517 A199216 A057620 * A102239 A188233 A319457

Adjacent sequences: A055622 A055623 A055624 * A055626 A055627 A055628

Keyword

nonn

Author

Labos Elemer, Jun 05 2000

Extensions

Corrected and extended by Reiner Martin, May 19 2001

More terms from Hugo Pfoertner, Jul 31 2003

a(20)>2^31, a(21)=1444257673. - Hugo Pfoertner, Jul 31 2003

More terms from Jens Kruse Andersen, May 30 2006

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 27 2006

Status

approved