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%I #29 Oct 30 2022 18:19:59
%S 7,31,151,3049,7351,1741,19471,118801,498259,148531,406951,2513803,
%T 2339041,89089369,51662593,73451737,232301497,450988159,1558562197,
%U 2506152301,1444257673,28265029657,24061965043,87996684091,43553959717
%N First prime starting a chain of exactly n consecutive primes congruent to 1 modulo 6.
%C 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.
%C See A057620 for the variant where "exactly" is replaced by "at least". - _M. F. Hasler_, Sep 03 2016
%H Giovanni Resta, <a href="/A055625/b055625.txt">Table of n, a(n) for n = 1..35</a> (terms < 4*10^14)
%H J. K. Andersen, <a href="http://primerecords.dk/congruent-primes.htm">Consecutive Congruent Primes</a>.
%H A. Granville and G. Martin, <a href="http://www.arXiv.org/abs/math.NT/0408319">Prime number races</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
%t pp = Table[{p = Prime[n], Mod[p, 6]}, {n, 10^6}];
%t sp = Split[pp, Mod[#1[[2]], 6] == Mod[#2[[2]], 6]&];
%t a[n_] := SelectFirst[sp, Length[#] == n && MatchQ[#, {{_Integer, 1} ..}]& ][[1, 1]];
%t Table[an = a[n]; Print[n, " ", an]; an, {n, 1, 13}] (* _Jean-François Alcover_, Nov 21 2018 *)
%o See link in A085515.
%Y Cf. A055623, A055624, A055626, A085515.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 05 2000
%E Corrected and extended by _Reiner Martin_, May 19 2001
%E More terms from _Hugo Pfoertner_, Jul 31 2003
%E a(20)>2^31, a(21)=1444257673. - _Hugo Pfoertner_, Jul 31 2003
%E More terms from _Jens Kruse Andersen_, May 30 2006
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 27 2006
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