A297356 Values of n for which pi_{12,7}(p_n) - pi_{12,1}(p_n) = -1, where p_n is the n-th prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

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

Offset: 1

Author

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

Keywords

• nonn

Comments

This is a companion sequence to A297357 and includes the values of n for 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).

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 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