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

Author

Yasutoshi Kohmoto, Aug 12 2004

Keywords

• nonn

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

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.

Crossrefs

Cf. A096447-A096455.

Cf. A002144, A002145, A007350, A007351

Programs

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

Extensions

More terms from Joshua Zucker, May 03 2006