A096628 -id:A096628 - cp's OEIS frontend

A297355 Primes p for which pi_{12,5}(p) - pi_{12,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

25726067172577, 25726067172857, 25726067173321, 25726067173441, 25726067174389, 25726067174461, 25726067174653, 25726067174761, 25726067175961, 25726067176549, 25726067176669, 25726067176993, 25726067177149, 25726067177429, 25726067177449, 25726067177593, 25726067177617, 25726067177689, 25726067177801, 25726067178013

Offset: 1

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 29 2017

nonn

This is a companion sequence to A297354 and includes the first discovered sign-changing zone for pi_{12,5}(p) - pi_{12,1}(p) prime race. The full sequence checked up to 10^14 has 8399 terms (see b-file).

Sergei D. Shchebetov, Table of n, a(n) for n = 1..8399
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.
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. A007350, A007351, A038691, A051024, A066520, A096628, A096447, A096448, A199547, A297354.

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

A297355 Primes p for which pi_{12,5}(p) - pi_{12,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

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