This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A297006 #15 May 27 2025 10:08:50
%S A297006 608981813029,608981813137,608981813261,608981813273,608981813311,
%T A297006 608981813357,608981813459,608981813683,608981813717,608981813777,
%U A297006 608981813789,608981814127,608981818999,608981819021,608981819273,608981819359,608981819419,608981820869,608981820899,608981820913,608981826877,608981827873,608981827891,608981828023,608981828029,608981828111,608981828129,608981836363,608981836391,608981836481
%N 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).
%C A297006 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).
%H A297006 Sergei D. Shchebetov, <a href="/A297006/b297006.txt">Table of n, a(n) for n = 1..84323</a>
%H A297006 A. Alahmadi, M. Planat, and P. Solé, <a href="https://hal.archives-ouvertes.fr/hal-00650320">Chebyshev's bias and generalized Riemann hypothesis</a>, HAL Id: hal-00650320.
%H A297006 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 A297006 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 A297006 M. Deléglise, P. Dusart, and 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 A297006 A. Granville and G. Martin, <a href="https://web.archive.org/web/20240529054811/https://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 A297006 M. Rubinstein and 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 A297006 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeQuadraticEffect.html">Prime Quadratic Effect.</a>
%Y A297006 Cf. A007352, A096629, A096630, A096449, A098044.
%K A297006 nonn
%O A297006 1,1
%A A297006 Andrey S. Shchebetov and _Sergei D. Shchebetov_, Dec 23 2017