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%I #14 Apr 19 2016 01:07:34
%S 5,11,17,23,41,47,83,167,227,233,608981812919,608981812961,
%T 608981813017,608981813569,608981813677,608981813833,608981813851,
%U 608981813927,608981813939,608981813963,608981814043,608981814149,608981814251,608981814827
%N Primes p such that the number of primes q, 5 <= q < p, congruent to 1 mod 3, is equal to the number of such primes congruent to 2 mod 3.
%C First term prime(3) = 5 is placed on 0th row.
%C If prime(n-1) = +1 mod 3 is on k-th row then we put prime(n) on (k-1)-st row.
%C If prime(n-1) = -1 mod 3 is on k-th row then we put prime(n) on (k+1)-st row.
%C This process makes an array of prime numbers:
%C 5, 11, 17, 23, 41, 47, 83, ... (this sequence)
%C 7, 13, 19, 29, 37, 43, 53, 71, 79, 89, 101, .. (A096452).
%C 31, 59, 67, 73, 97, ... (A096453)
%C 61, ...
%F For n>1, a(n) = prime(A096629(n-1)+1) = A000040(A096629(n-1)+1). - _Max Alekseyev_, Sep 19 2009
%F a(n) = A151800(A098044(n)) = A007918(A098044(n)+1).
%t lst = {5}; p = 0; q = 0; r = 5; While[r < 10^9, If[ Mod[r, 3] == 2, p++, q++ ]; r = NextPrime@r; If[p == q, AppendTo[lst, r]; Print@r]]; lst (* _Robert G. Wilson v_, Sep 20 2009 *)
%Y Cf. A096448-A096455.
%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(11) onward from _Max Alekseyev_, Feb 10 2011
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