A297006 -id:A297006 - cp's OEIS frontend

A096630 Numbers n for which the set of first n primes (mod 3) is biased towards 1.

23338590792, 23338590794, 23338590795, 23338590796, 23338590797, 23338590798, 23338590800, 23338590801, 23338590802, 23338590803, 23338590804, 23338590810, 23338590811, 23338590812, 23338590813

Offset: 1

Eric W. Weisstein, Jul 01 2004

nonn

Indices of negative terms in A112632. - Jianing Song, Feb 20 2019

C. Bays, R. H. Hudson, Details of the First Region of Integers x with pi_{3,2}(x) < pi_{3,1}(x), Mathematics of Computation 32(142), 1978, pp. 571-576.
Eric Weisstein's World of Mathematics, Chebyshev Bias

Cf. A096629, A007352, A112632, A297005, A297006.

Edited by Max Alekseyev, Sep 13 2009

A297005 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).

Original entry on oeis.org

23338590792, 23338590794, 23338590796, 23338590798, 23338590800, 23338590802, 23338590804, 23338590810, 23338590814, 23338590816, 23338590818, 23338590832, 23338591016, 23338591018, 23338591028, 23338591030, 23338591032, 23338591084, 23338591086, 23338591088, 23338591302, 23338591340, 23338591342, 23338591344, 23338591346, 23338591348, 23338591350, 23338591656, 23338591658, 23338591662

Offset: 1

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 23 2017

nonn

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).

Sergei D. Shchebetov, Table of n, a(n) for n = 1..84323
A. Alahmadi, M. Planat, and 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, and X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp. 1565-1575.
A. Granville and G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.
M. Rubinstein and P. Sarnak, Chebyshev's bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173-197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect.

Cf. A007352, A096629, A096630, A096449, A098044.

A306891 Primes p for which pi_{3,2}(p) < pi_{3,1}(p), where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

Original entry on oeis.org

608981813029, 608981813137, 608981813191, 608981813261, 608981813269, 608981813273, 608981813311, 608981813347, 608981813357, 608981813449, 608981813459, 608981813683, 608981813701, 608981813707, 608981813711, 608981813717, 608981813719, 608981813777, 608981813779

Offset: 1

Jianing Song, Mar 16 2019

nonn

Primes p such that Sum_{primes q <= p} Kronecker(-3,q) > 0.

Indices of negative terms in A321856. See also the comment about Chebyshev's bias in A321856.

David A. Corneth, Table of n, a(n) for n = 1..10000
C. Bays, R. H. Hudson, Details of the First Region of Integers x with pi_{3,2}(x) < pi_{3,1}(x), Mathematics of Computation 32(142), 1978, pp. 571-576.
Eric Weisstein's World of Mathematics, Chebyshev Bias
Wikipedia, Chebyshev's bias

Cf. A096630, A112632, A297006, A321856.

Cf. also A199547, A096628.

my(i=0); forprime(p=608981813029, 608981820000, i+=kronecker(-3, p); if(i>0, print1(p, ", ")))

a(n) = prime(A096630(n)).

cp's OEIS Frontend

A096630 Numbers n for which the set of first n primes (mod 3) is biased towards 1.

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A297005 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).

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A306891 Primes p for which pi_{3,2}(p) < pi_{3,1}(p), where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

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