

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



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

1,1


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) signchanging zone contains 234937 terms (see afile) 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, P. Solé, Chebyshev's bias and generalized Riemann hypothesis, HAL Id: hal00650320.
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. 111119, 1979.
C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, Zeros of Dirichlet Lfunctions near the real axis and Chebyshev's bias, J. Number Theory 87 (2001), pp.5476.
M. Deléglise, P. Dusart, X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.15651575.
A. Granville, G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 133.
M. Rubinstein, P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect.


CROSSREFS

Cf. A007350, A007351, A038691, A051024, A051025, A066520, A096628, A096447, A096448, A199547, A275939, A295354.
Sequence in context: A288278 A172566 A214947 * A086439 A086440 A216906
Adjacent sequences: A295351 A295352 A295353 * A295355 A295356 A295357


KEYWORD

nonn


AUTHOR

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


STATUS

approved



