A296021 Number of primes of the form 4*k+1 <= 4*n+1.

0, 1, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 12, 12, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 19, 19, 19, 20, 21, 21, 21, 21, 21, 21, 21, 21, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 28, 28

Offset: 0

Author

Seiichi Manyama, Dec 02 2017

Keywords

• nonn

References

• G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 23.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A016813, A091098, A295996, A296020.

Programs

Mathematica

a[n_]:=Length[Select[Range[n],PrimeQ[4#+1] &]]; Array[a,72,0] (* Stefano Spezia, May 01 2025 *)

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
p A(1, 100)