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%I #12 Sep 30 2017 02:33:35
%S 7,241,967,15787,111577,1587499,25230061,118194961,188698981,761453863
%N Smallest prime = 1 mod 6 sandwiched by n smaller and n larger primes = 5 mod 6.
%C Is the sequence infinite?
%H A. Granville and G. Martin, <a href="https://arxiv.org/abs/math/0408319">Prime number races</a>, arXiv:math/0408319 [math.NT], 2004.
%H A. Granville and G. Martin, <a href="http://www.jstor.org/stable/27641834">Prime number races</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
%F a(n) = (smallest p(m) = 1 mod 6) such that all 2*n primes p(m-n..m-1) and p(m+1..m+n) = 5 mod 6.
%e a(n) = 7 is sandwiched by primes 5 and 11 (both primes = 5 mod 6),
%e a(2) = 241 is sandwiched by 2 lesser primes 233, 239 and 2 larger primes 251, 257 (all four primes = 5 mod 6),
%e a(3) = 967 is sandwiched by 3 lesser primes 941, 947, 953 and 3 larger primes 971, 977, 983 (all six primes = 5 mod 6),
%e a(4) = 15787 is sandwiched by 4 lesser primes 15749, 15761, 15767, 15773 and 4 larger primes 15791, 15797, 15803, 15809 (all 8 primes = 5 mod 6),
%e a(5) = 111577 is sandwiched by 5 lesser primes 111497, 111509, 111521, 111533, 111539 and 5 larger primes 111581, 111593, 111599, 111611, 111623 (all 10 primes = 5 mod 6), etc.
%K nonn,more
%O 1,1
%A _Zak Seidov_, Mar 19 2012
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