A096448 Primes p such that the number of primes less than p equal to 1 mod 4 is one less than the number of primes less than p equal to 3 mod 4.

5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, 419, 431, 439, 461, 467, 1259, 1279, 1303, 26833, 26849, 26881, 26893, 26921, 26947, 615883, 616769, 616787, 616793, 616829, 617051, 617059, 617087, 617257, 617473, 617509, 617647, 617681, 617731, 617819, 617879

Offset

1,1

Comments

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

Links

Michel Marcus, Table of n, a(n) for n = 1..751

Example

First term prime(2) = 3 is placed on 0th row.
If prime(n-1) = +1 mod 4 is on k-th row then we put prime(n) on (k-1)-st row.
If prime(n-1) = -1 mod 4 is on k-th row then we put prime(n) on (k+1)-st row.
This process makes an array of prime numbers:
  0th row:  3,  7, 19,  43, ...
  1st row:  5, 11, 17,  23, 31, 41, 47, 59, 67, 103, 127, ...
  2nd row: 13, 29, 37,  53, 61, 71, 79, 101, 107, 113 ...
  3rd row: 73, 83, 97, 109, ...
  4th row: 89, ...

Mathematica

Prime[#]&/@(Flatten[Position[Accumulate[If[Mod[#, 4]==1, 1, -1]&/@ Prime[ Range[ 2, 51000]]], -1]]+2) (* Harvey P. Dale, Mar 08 2015 *)

Prog

(PARI) lista(nn) = my(vp=primes(nn), nb1=0, nb3=0); for (i=2, #vp, my(p = vp[i]); if (nb1 == nb3-1, print1(p, ", ")); if ((p % 4) == 1, nb1++, nb3++); ); \\ Michel Marcus, May 30 2024

Crossrefs

Sequence of the same family: A096447, A096451.

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

Sequence in context: A189938 A184525 A252596 * A351140 A365809 A147305

Adjacent sequences: A096445 A096446 A096447 * A096449 A096450 A096451

Keyword

nonn

Author

Yasutoshi Kohmoto, Aug 12 2004

Extensions

More terms from Joshua Zucker, May 03 2006

Status

approved