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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
192252423729713, 192252423730849, 192252423731231, 192252423731633, 192252423731663, 192252423731839, 192252423732311, 192252423769201, 192252423769361, 192252423769537, 192252423772649, 192252423772807, 192252423772847, 192252423774023, 192252423774079, 192252423774457, 192252423779257, 192252423782521, 192252423783263, 192252423783551 (list; graph; refs; listen; history; text; internal format)
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) 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, 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, 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
Sequence in context: A172566 A214947 A364413 * A086439 A086440 A216906
KEYWORD
nonn
AUTHOR
Andrey S. Shchebetov and Sergei D. Shchebetov, Nov 20 2017
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)