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).

192252423729713, 192252423730849, 192252423731231, 192252423731633, 192252423731663, 192252423731839, 192252423732311, 192252423769201, 192252423769361, 192252423769537, 192252423772649, 192252423772807, 192252423772847, 192252423774023, 192252423774079, 192252423774457, 192252423779257, 192252423782521, 192252423783263, 192252423783551

Offset: 1

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Nov 20 2017

Keywords

• nonn

Comments

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).

Links

• Andrey S. Shchebetov and Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000
• A. Alahmadi, M. Planat, and P. Solé, Chebyshev's bias and generalized Riemann hypothesis, HAL Id: hal-00650320.
• C. Bays and R. H. Hudson, Numerical and graphical description of all axis crossing regions for moduli 4 and 8 which occur before 10^12, International Journal of Mathematics and Mathematical Sciences, vol. 2, no. 1, pp. 111-119, 1979.
• 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.
• M. Deléglise, P. Dusart, and X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.1565-1575.
• A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
• M. Rubinstein and P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173-197.
• Eric Weisstein's World of Mathematics, Prime Quadratic Effect.

Crossrefs

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