

A297356


Values of n for which pi_{12,7}(p_n)  pi_{12,1}(p_n) = 1, where p_n is the nth prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).


2



919096512484, 919096512490, 919096512492, 919096512496, 919096512500, 919096512504, 919096512517, 919096512519, 919096512648, 919096512655, 919096512662, 919096512718, 919096512725, 919096512729, 919096512741, 919096512744, 919096512747, 919096512753, 919096512798, 919096512802
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OFFSET

1,1


COMMENTS

This is a companion sequence to A297357 and includes the values of n for the first discovered signchanging zone for pi_{12,7}(p)  pi_{12,1}(p) prime race. The full sequence checked up to 10^14 has 55596 terms (see bfile).


LINKS

Sergei D. Shchebetov, Table of n, a(n) for n = 1..55596
C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, Zeros of Dirichlet Lfunctions near the real axis and Chebyshev's bias, J. Number Theory 87 (2001), pp. 5476.
A. Granville, G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 133.
M. Rubinstein, P. Sarnak, Chebyshev's bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect


CROSSREFS

Sequence in context: A186017 A015433 A234195 * A172853 A295356 A180616
Adjacent sequences: A297353 A297354 A297355 * A297357 A297358 A297359


KEYWORD

nonn


AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 29 2017


STATUS

approved



