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

1,1

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, ...

Primes prime(n) such that A038698(n-1) = 0. In other words, p such that A066520(prevprime(p)) = 0. - Jianing Song, Jan 06 2026

Links

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

Formula

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

a(n) = prime(A038691(n)+1). - Jianing Song, Jan 06 2026

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 *)

Crossrefs

Sequence of the same family: A096448, A096451.

Cf. A007351, A038691, A151800.

See also A096449, A096452, A096453, A096450, A096454, A096455.

Sequence in context: A136041 A146685 A146653 * A274596 A374728 A348008

Adjacent sequences: A096444 A096445 A096446 * A096448 A096449 A096450

Keyword

nonn,easy

Author

Yasutoshi Kohmoto, Aug 12 2004

Extensions

More terms from Joshua Zucker, May 03 2006

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

Status

approved