A297357 - OEIS

%I #6 Feb 16 2025 08:33:52

%S 27489101529529,27489101529679,27489101529727,27489101529847,

%T 27489101529991,27489101530159,27489101530699,27489101530747,

%U 27489101534611,27489101535037,27489101535229,27489101536843,27489101537101,27489101537281,27489101537761,27489101537827,27489101538007,27489101538163,27489101539591,27489101539723

%N 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).

%C 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).

%H Sergei D. Shchebetov, <a href="/A297357/b297357.txt">Table of n, a(n) for n = 1..55596</a>

%H C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, <a href="https://doi.org/10.1006/jnth.2000.2601">Zeros of Dirichlet L-functions near the real axis and Chebyshev's bias</a>, J. Number Theory 87 (2001), pp. 54-76.

%H A. Granville, G. Martin, <a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/granville1.pdf">Prime Number Races</a>, Amer. Math. Monthly 113 (2006), no. 1, 1-33.

%H M. Rubinstein, P. Sarnak, <a href="https://projecteuclid.org/euclid.em/1048515870">Chebyshev's bias</a>, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeQuadraticEffect.html">Prime Quadratic Effect</a>

%K nonn,changed

%O 1,1

%A Andrey S. Shchebetov and _Sergei D. Shchebetov_, Dec 29 2017