A267097 a(n) = number of 4k+1 primes among first n primes; least monotonic left inverse of A080147.

0, 0, 1, 1, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 11, 12, 12, 12, 13, 14, 14, 14, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 20, 21, 21, 21, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 29, 30, 31, 31, 32, 32, 33, 34, 34, 34, 35, 35, 35, 36, 37, 38, 39, 39, 40, 40, 41

Offset: 1

Author

Antti Karttunen, Feb 01 2016

Keywords

• nonn

Comments

a(n) = number of 4k+1 primes (A002144) among primes in range 2 .. A000040(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000040, A002144, A080147, A267098.

Cf. also A267101.

Programs

Mathematica

a[n_]:=Length[Select[Prime[Range[n]],IntegerQ[(#-1)/4] &]]; Array[a,84] (* Stefano Spezia, May 01 2025 *)

Formula

Other identities. For all n >= 1:

a(A080147(n)) = n.

a(n) + A267098(n) = n-1.