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A295354 Primes p for which pi_{8,7}(p) - pi_{8,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m). 3


%S 192252423729713,192252423730849,192252423731231,192252423731633,

%T 192252423731663,192252423731839,192252423732311,192252423769201,

%U 192252423769361,192252423769537,192252423772649,192252423772807,192252423772847,192252423774023,192252423774079,192252423774457,192252423779257,192252423782521,192252423783263,192252423783551

%N Primes p for which pi_{8,7}(p) - pi_{8,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

%C This sequence is a companion sequence to A295353. The sequence with the first found pi_{8,7}(p_n) - pi_{8,1}(p_n) sign-changing zone contains 234937 terms (see a-file) with a(237937) = 192876135747311 as its last term. In addition, a(1) = A275939(8).

%H Andrey S. Shchebetov and Sergei D. Shchebetov, <a href="/A295354/b295354.txt">Table of n, a(n) for n = 1..100000</a>

%H A. Alahmadi, M. Planat, P. Solé, <a href="https://hal.archives-ouvertes.fr/hal-00650320">Chebyshev's bias and generalized Riemann hypothesis</a>, HAL Id: hal-00650320.

%H C. Bays and R. H. Hudson, <a href="http://dx.doi.org/10.1155/S0161171279000119">Numerical and graphical description of all axis crossing regions for moduli 4 and 8 which occur before 10^12</a>, International Journal of Mathematics and Mathematical Sciences, vol. 2, no. 1, pp. 111-119, 1979.

%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 M. Deléglise, P. Dusart, X. Roblot, <a href="http://dx.doi.org/10.1090/S0025-5718-04-01649-7">Counting Primes in Residue Classes</a>, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.1565-1575.

%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, Pages 173-197.

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

%Y Cf. A007350, A007351, A038691, A051024, A051025, A066520, A096628, A096447, A096448, A199547, A275939, A295354.

%K nonn

%O 1,1

%A Andrey S. Shchebetov and _Sergei D. Shchebetov_, Nov 20 2017

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)