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

Author

Yasutoshi Kohmoto, Aug 12 2004

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A096447-A096455, A096629, A098044.

Programs

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 *)

Extensions

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

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