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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.
4

%I #17 Apr 19 2016 01:07:34

%S 7,13,19,29,37,43,53,71,79,89,101,107,113,131,163,173,223,229,239,251,

%T 383,443,1811,1871,1877,1889,608981812613,608981812667,608981812891,

%U 608981812951,608981812993,608981813929,608981813941,608981814019,608981814173

%N 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.

%H A. Granville, G. Martin, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimeRace.pdf">Prime number races</a>, Amer. Math. Monthly vol 113, no 1 (2006) p 1.

%H G. D. Martin, <a href="http://www.math.umn.edu/~focm/c_/Martin.pdf">Biases in the Shanks-Renyi prime number race</a>, FoCM'02 Conference, Minneapolis, 5-14 Aug 2002.

%t 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 *)

%Y Cf. A096447-A096455, A096629, A098044.

%K nonn

%O 1,1

%A _Yasutoshi Kohmoto_, Aug 12 2004

%E More terms and better definition from _Joshua Zucker_, May 21 2006

%E Terms a(27) onward from _Max Alekseyev_, Feb 10 2011