A096449 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.

5, 11, 17, 23, 41, 47, 83, 167, 227, 233, 608981812919, 608981812961, 608981813017, 608981813569, 608981813677, 608981813833, 608981813851, 608981813927, 608981813939, 608981813963, 608981814043, 608981814149, 608981814251, 608981814827

Offset: 1

Author

Yasutoshi Kohmoto, Aug 12 2004

Keywords

• nonn

Comments

First term prime(3) = 5 is placed on 0th row.

If prime(n-1) = +1 mod 3 is on k-th row then we put prime(n) on (k-1)-st row.

If prime(n-1) = -1 mod 3 is on k-th row then we put prime(n) on (k+1)-st row.

This process makes an array of prime numbers:

5, 11, 17, 23, 41, 47, 83, ... (this sequence)

7, 13, 19, 29, 37, 43, 53, 71, 79, 89, 101, .. (A096452).

31, 59, 67, 73, 97, ... (A096453)

61, ...

Crossrefs

Cf. A096448-A096455.

Programs

Mathematica

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 *)

Formula

For n>1, a(n) = prime(A096629(n-1)+1) = A000040(A096629(n-1)+1). - Max Alekseyev, Sep 19 2009

a(n) = A151800(A098044(n)) = A007918(A098044(n)+1).

Extensions

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

Terms a(11) onward from Max Alekseyev, Feb 10 2011