OFFSET
1,1
COMMENTS
This is a companion sequence to A297447. The first two sign-changing 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 a-file) with a(664175) = 194318969449909 as its last term.
This sequence was checked up to 10^15 and the 7th sign-changing 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. 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, X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.1565-1575.
A. Granville, G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
M. Rubinstein, 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
KEYWORD
nonn
AUTHOR
Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 30 2017
STATUS
approved