A096451 Primes p such that the number of primes less than p equal to 1 mod 4 is two less than the number of primes less than p equal to 3 mod 4.

13, 29, 37, 53, 61, 71, 79, 101, 107, 113, 131, 139, 151, 163, 199, 359, 409, 421, 433, 443, 457, 479, 1223, 1231, 1249, 1277, 1283, 1291, 1301, 1307, 1399, 1423, 1439, 8699, 8779, 26821, 26951, 26959, 26987, 27011, 27031, 615731, 615869, 615887

Offset

1,1

Comments

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:

3, 7, 19, 43, ....0th row

5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ....first row

13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ....2nd row

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

89, ....4th row

Primes prime(n) such that A038698(n-1) = 2. In other words, p such that A066520(prevprime(p)) = 2. - Jianing Song, Jan 06 2026

Links

Robert Israel, Table of n, a(n) for n = 1..811

Andrew Granville and Greg Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

Maple

c1:= 0; c3:= 0: p:= 2: count:= 0: Res:= NULL:
while count < 100 do
  p:= nextprime(p);
  if c1 = c3 - 2 then
    count:= count+1;
    Res:= Res, p;
  fi;
  if p mod 4 = 1 then c1:=c1+1
  else c3:= c3+1
  fi
od:
Res; # Robert Israel, Nov 07 2018

Crossrefs

Sequence of the same family: A096447, A096451.

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

Cf. A002144, A002145, A007350, A007351.

Sequence in context: A340919 A345705 A322388 * A090690 A160026 A141555

Adjacent sequences: A096448 A096449 A096450 * A096452 A096453 A096454

Keyword

nonn

Author

Yasutoshi Kohmoto, Aug 12 2004

Extensions

More terms from Joshua Zucker, May 03 2006

Status

approved