A096447 Odd primes p such that the number of primes less than p that are congruent to 1 (mod 4) is equal to the number of primes less than p that are congruent to 3 (mod 4).

3, 7, 19, 43, 463, 26839, 26861, 26879, 26891, 26903, 26927, 616783, 616799, 616841, 616849, 616877, 617039, 617269, 617369, 617401, 617429, 617453, 617471, 617479, 617521, 617537, 617587, 617689, 617717, 617723, 618439, 618547, 618619, 618643

Offset: 1

Author

Yasutoshi Kohmoto, Aug 12 2004

Keywords

• nonn
• easy

Comments

Assign the odd prime numbers to the rows of an array as follows:

Assign the first odd prime, prime(2) = 3, to row 0 (the top row).

For m > 2, assign prime(m) to the row immediately above or below the row to which prime(m-1) was assigned: above if prime(m-1) == 1 (mod 4), below otherwise.

The following array results:

row 0 (this sequence): 3, 7, 19, 43, 463, 26839, ...

row 1 (A096448): 5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ...

row 2 (A096451): 13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ...

row 3: 73, 83, 97, 109, ...

row 4: 89, ...

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007351, A151800.

Cf. A096448, A096449, A096450, A096451, A096452, A096453, A096454, A096455.

Programs

Mathematica

lim = 10^5; k1 = 0; k3 = 0; p = 2; t = {}; Do[p = NextPrime[p]; If[k1 == k3, AppendTo[t, p]]; If[Mod[p, 4] == 1, k1++, k3++], {lim}]; t (* T. D. Noe, Sep 07 2011 *)

Formula

a(n) = A151800(A007351(n)), the next prime after A007351(n). - Joshua Zucker, May 03 2006

Extensions

More terms from Joshua Zucker, May 03 2006

"odd" added to definition by N. J. A. Sloane, Sep 09 2015