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A297006
Primes p for which pi_{3,2}(p) - pi_{3,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).
4
608981813029, 608981813137, 608981813261, 608981813273, 608981813311, 608981813357, 608981813459, 608981813683, 608981813717, 608981813777, 608981813789, 608981814127, 608981818999, 608981819021, 608981819273, 608981819359, 608981819419, 608981820869, 608981820899, 608981820913, 608981826877, 608981827873, 608981827891, 608981828023, 608981828029, 608981828111, 608981828129, 608981836363, 608981836391, 608981836481
OFFSET
1,1
COMMENTS
This sequence is a companion sequence to A297005. Starting from a(20591)=6148171711663 the sequence includes the second sign-changing zone predicted by C. Bays et al. in 2001. The sequence with the first two sign-changing zones up to 10^13 contains 84323 terms with a(84323)=6156051951677 as its last term (see b-file). In addition, a(1) = A007352(2) as well as a(20591) = A007352(9630).
LINKS
Sergei D. Shchebetov, Table of n, a(n) for n = 1..84323
A. Alahmadi, M. Planat, P. Solé, Chebyshev's bias and generalized Riemann hypothesis, HAL Id: hal-00650320.
C. Bays and R. H. Hudson, Details of the first region of integers x with pi_{3,2} (x) < pi_{3,1}(x), Math. Comp. 32 (1978), 571-576
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, pp. 173-197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect.
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 23 2017
STATUS
approved