A297354 Values of n for which pi_{12,5}(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).

862062606318, 862062606330, 862062606348, 862062606351, 862062606377, 862062606380, 862062606387, 862062606393, 862062606424, 862062606448, 862062606453, 862062606466, 862062606469, 862062606478, 862062606481, 862062606488, 862062606490, 862062606494, 862062606496, 862062606500

Offset

1,1

Comments

This is a companion sequence to A297355 and includes values of n for the first discovered sign-changing zone for pi_{12,5}(p) - pi_{12,1}(p) prime race. The full sequence checked up to 10^14 has 8399 terms (see b-file).

Links

Sergei D. Shchebetov, Table of n, a(n) for n = 1..8399

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, G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.

M. Rubinstein, P. Sarnak, Chebyshev's bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.

Eric Weisstein's World of Mathematics, Prime Quadratic Effect

Crossrefs

Cf. A007350, A007351, A038691, A051024, A066520, A096628, A096447, A096448, A199547, A297355.

Sequence in context: A162027 A172616 A233487 * A172798 A186017 A015433

Adjacent sequences: A297351 A297352 A297353 * A297355 A297356 A297357

Keyword

nonn

Author

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

Status

approved