|
%I #13 Dec 26 2017 17:29:56
%S 23338590792,23338590794,23338590796,23338590798,23338590800,
%T 23338590802,23338590804,23338590810,23338590814,23338590816,
%U 23338590818,23338590832,23338591016,23338591018,23338591028,23338591030,23338591032,23338591084,23338591086,23338591088,23338591302,23338591340,23338591342,23338591344,23338591346,23338591348,23338591350,23338591656,23338591658,23338591662
%N Values of n for which pi_{3,2}(p_n) - pi_{3,1}(p_n) = -1, where p_n is the n-th prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).
%C This sequence is a companion sequence to A297006. Starting from a(20591)=216415270060 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)=216682882512 as its last term (see b-file). In addition, a(1) = A096630(1).
%H Sergei D. Shchebetov, <a href="/A297005/b297005.txt">Table of n, a(n) for n = 1..84323</a>
%H A. Alahmadi, M. Planat, P. Solé, <a href="https://hal.archives-ouvertes.fr/hal-00650320">Chebyshev's bias and generalized Riemann hypothesis</a>, HAL Id: hal-00650320.
%H C. Bays and R. H. Hudson, <a href="https://doi.org/10.1090/S0025-5718-1978-0476616-X">Details of the first region of integers x with pi_{3,2} (x) < pi_{3,1}(x)</a>, Math. Comp. 32 (1978), 571-576.
%H C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, <a href="https://doi.org/10.1006/jnth.2000.2601">Zeros of Dirichlet L-functions near the real axis and Chebyshev's bias</a>, J. Number Theory 87 (2001), pp. 54-76.
%H M. Deléglise, P. Dusart, X. Roblot, <a href="http://dx.doi.org/10.1090/S0025-5718-04-01649-7">Counting Primes in Residue Classes</a>, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp. 1565-1575.
%H A. Granville, G. Martin, <a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/granville1.pdf">Prime Number Races</a>, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
%H M. Rubinstein, P. Sarnak, <a href="https://projecteuclid.org/euclid.em/1048515870">Chebyshev's bias</a>, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeQuadraticEffect.html">Prime Quadratic Effect.</a>
%Y Cf. A007352, A096629, A096630, A096449, A098044.
%K nonn
%O 1,1
%A Andrey S. Shchebetov and _Sergei D. Shchebetov_, Dec 23 2017
|
