A297355 - OEIS

%I #9 Feb 16 2025 08:33:52

%S 25726067172577,25726067172857,25726067173321,25726067173441,

%T 25726067174389,25726067174461,25726067174653,25726067174761,

%U 25726067175961,25726067176549,25726067176669,25726067176993,25726067177149,25726067177429,25726067177449,25726067177593,25726067177617,25726067177689,25726067177801,25726067178013

%N Primes p for which pi_{12,5}(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 A297354 and includes 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 Sergei D. Shchebetov, <a href="/A297355/b297355.txt">Table of n, a(n) for n = 1..8399</a>

%H C. Bays and R. H. Hudson, <a href="https://doi.org/10.1090/S0025-5718-1978-0476616-X">Details of the first region of integers x with pi_{3,2} (x) < pi_{3,1}(x)</a>, Math. Comp. 32 (1978), 571-576.

%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>

%Y Cf. A007350, A007351, A038691, A051024, A066520, A096628, A096447, A096448, A199547, A297354.

%K nonn

%O 1,1

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