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).

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

Offset: 1

Author

Jianing Song, Mar 16 2019

Keywords

• nonn

Comments

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.

Links

• 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

Crossrefs

Cf. A096630, A112632, A297006, A321856.

Cf. also A199547, A096628.

Programs

PARI

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

Formula

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