

A297448


Primes p for which pi_{8,5}(p)  pi_{8,1}(p) = 1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).


2



588067889, 588068009, 588068093, 588068309, 588068333, 588068477, 588068717, 588069137, 588069169, 588069409, 588069529, 588069809, 588070897, 588070949, 588071009, 588071101, 588071401, 588071573, 588071597, 588079253
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OFFSET

1,1


COMMENTS

This is a companion sequence to A297447. The first two signchanging zones were discovered by Bays and Hudson back in 1979. We discovered four additional zones starting from a(22794) = 5267226902633. The full sequence with all 6 zones checked up to 5*10^14 contains 664175 terms (see afile) with a(664175) = 194318969449909 as its last term.
This sequence was checked up to 10^15 and the 7th signchanging zone starting from a(664176) = 930525161507057 and ending with a(850232)= 932080335660277 was found.  Andrey S. Shchebetov and Sergei D. Shchebetov, Jul 28 2018


LINKS

Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000
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. DelĂ©glise, 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, Chebyshevâ€™s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect.


CROSSREFS

Sequence in context: A186961 A032755 A234391 * A057535 A134858 A344928
Adjacent sequences: A297445 A297446 A297447 * A297449 A297450 A297451


KEYWORD

nonn


AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 30 2017


STATUS

approved



