A295996 One quarter of number of Gaussian primes whose norm is 4*n+1 or less.

0, 3, 4, 6, 8, 8, 8, 10, 10, 12, 14, 14, 15, 17, 17, 19, 19, 19, 21, 21, 21, 21, 23, 23, 25, 27, 27, 29, 31, 31, 32, 32, 32, 32, 34, 34, 34, 36, 36, 38, 38, 38, 38, 40, 40, 42, 42, 42, 44, 46, 46, 46, 46, 46, 46, 46, 46, 48, 50, 50, 52, 52, 52, 52, 54, 54, 54, 56

Offset: 0

Author

Seiichi Manyama, Dec 02 2017

Keywords

• nonn

Examples

			The Gaussian primes whose norm is 9 or less;
      *        3i,
    *   *      -1+2i, 1+2i
  * *   * *    -2+i, -1+i, 1+i, 2+i
*           *  -3, 3
  * *   * *    -2-i, -1-i, 1-i, 2-i
    *   *      -1-2i, 1-2i
      *        -3i
               a(2) = 16/4 = 4.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Gaussian Prime

Crossrefs

Cf. A016813, A055029, A091100, A091134, A135462, A296020, A296021.

Programs

Ruby

require 'prime'
def A(k, n)
  ary = []
  cnt = 0
  k.step(4 * n + k, 4){|i|
    cnt += 1 if i.prime?
    ary << cnt
  }
  ary
end
def A295996(n)
  ary1 = A(1, n)
  ary3 = A(3, Math.sqrt(n).to_i) + [0]
  [0] + (1..n).map{|i| 1 + 2 * ary1[i] + ary3[(Math.sqrt(4 * i + 1).to_i - 3) / 4]}
end
p A295996(100)