cp's OEIS Frontend

A210248 Smallest prime = 1 mod 6 sandwiched by n smaller and n larger primes = 5 mod 6.

%I A210248 #16 Sep 24 2024 03:13:25
%S A210248 7,241,967,15787,111577,1587499,25230061,118194961,188698981,
%T A210248 761453863,855198067,855198067,131320994401,473676340087,8775105756643
%N A210248 Smallest prime = 1 mod 6 sandwiched by n smaller and n larger primes  = 5 mod 6.
%C A210248 Is the sequence infinite?
%C A210248 Any further terms are > 10^13. - _Lucas A. Brown_, Sep 23 2024
%H A210248 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A210248.py">Python program</a>.
%H A210248 A. Granville and G. Martin, <a href="https://arxiv.org/abs/math/0408319">Prime number races</a>, arXiv:math/0408319 [math.NT], 2004.
%H A210248 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 A210248 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 A210248 a(n) = 7 is sandwiched by primes 5 and 11 (both primes = 5 mod 6),
%e A210248 a(2) = 241 is sandwiched by 2 lesser primes 233, 239  and 2 larger primes 251, 257 (all four primes = 5 mod 6),
%e A210248 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 A210248 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 A210248 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 A210248 nonn,more,hard
%O A210248 1,1
%A A210248 _Zak Seidov_, Mar 19 2012
%E A210248 a(11)-a(15) from _Lucas A. Brown_, Sep 23 2024