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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).

%I A297354 #12 May 27 2025 08:39:42
%S A297354 862062606318,862062606330,862062606348,862062606351,862062606377,
%T A297354 862062606380,862062606387,862062606393,862062606424,862062606448,
%U A297354 862062606453,862062606466,862062606469,862062606478,862062606481,862062606488,862062606490,862062606494,862062606496,862062606500
%N 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).
%C A297354 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).
%H A297354 Sergei D. Shchebetov, <a href="/A297354/b297354.txt">Table of n, a(n) for n = 1..8399</a>
%H A297354 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 A297354 A. Granville and G. Martin, <a href="https://web.archive.org/web/20240529054811/https://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 A297354 M. Rubinstein and 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 A297354 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeQuadraticEffect.html">Prime Quadratic Effect</a>
%Y A297354 Cf. A007350, A007351, A038691, A051024, A066520, A096628, A096447, A096448, A199547, A297355.
%K A297354 nonn
%O A297354 1,1
%A A297354 Andrey S. Shchebetov and _Sergei D. Shchebetov_, Dec 29 2017