A096452 Primes p such that the number of primes q, 5 <= q < p, congruent to 1 mod 3, is one less than the number of such primes congruent to 2 mod 3.

7, 13, 19, 29, 37, 43, 53, 71, 79, 89, 101, 107, 113, 131, 163, 173, 223, 229, 239, 251, 383, 443, 1811, 1871, 1877, 1889, 608981812613, 608981812667, 608981812891, 608981812951, 608981812993, 608981813929, 608981813941, 608981814019, 608981814173

Offset

1,1

Comments

Primes prime(n) such that A112632(n-1) = 2. In other words, p >= 5 such that A321856(prevprime(p)) = 2. - Jianing Song, Jan 06 2026

Links

Table of n, a(n) for n=1..35.

A. Granville, G. Martin, Prime number races, Amer. Math. Monthly vol 113, no 1 (2006) p 1.

G. D. Martin, Biases in the Shanks-Renyi prime number race, FoCM'02 Conference, Minneapolis, 5-14 Aug 2002.

Mathematica

lst = {}; p = q = 0; r = 5; While[r < 10^5, If[ Mod[r, 3] == 2, p++, q++ ]; r = NextPrime@ r; If[p == q + 1, AppendTo[lst, r]; Print@ r]]; lst (* Robert G. Wilson v, Sep 20 2009 *)

Crossrefs

Sequence of the same family: A096449, A096453.

See also A096447, A096448, A096451, A096450, A096454, A096455.

Cf. A096629, A098044.

Sequence in context: A211431 A379479 A299928 * A258038 A059647 A059310

Adjacent sequences: A096449 A096450 A096451 * A096453 A096454 A096455

Keyword

nonn

Author

Yasutoshi Kohmoto, Aug 12 2004

Extensions

More terms and better definition from Joshua Zucker, May 21 2006

Terms a(27) onward from Max Alekseyev, Feb 10 2011

Status

approved