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

1,1

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, ...

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

Links

Table of n, a(n) for n=1..24.

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).

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 *)

Crossrefs

Sequence of the same family: A096452, A096453.

Cf. A096629, A098044.

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

Sequence in context: A365809 A147305 A049755 * A268640 A360542 A214912

Adjacent sequences: A096446 A096447 A096448 * A096450 A096451 A096452

Keyword

nonn

Author

Yasutoshi Kohmoto, Aug 12 2004

Extensions

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

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

Status

approved