A297356 -id:A297356 - cp's OEIS frontend

A297357 Primes p for which pi_{12,7}(p) - pi_{12,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

27489101529529, 27489101529679, 27489101529727, 27489101529847, 27489101529991, 27489101530159, 27489101530699, 27489101530747, 27489101534611, 27489101535037, 27489101535229, 27489101536843, 27489101537101, 27489101537281, 27489101537761, 27489101537827, 27489101538007, 27489101538163, 27489101539591, 27489101539723

Offset: 1

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

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This is a companion sequence to A297356 and includes the first discovered sign-changing zone for pi_{12,7}(p) - pi_{12,1}(p) prime race. The full sequence checked up to 10^14 has 55596 terms (see b-file).

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 L-functions near the real axis and Chebyshev's bias, J. Number Theory 87 (2001), pp. 54-76.
A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
M. Rubinstein and P. Sarnak, Chebyshev's bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect

cp's OEIS Frontend

A297357 Primes p for which pi_{12,7}(p) - pi_{12,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

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