A267097 - OEIS

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A267097

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

9

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,6

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

FORMULA

Other identities. For all n >= 1:

a(A080147(n)) = n.

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

MATHEMATICA

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

PROG

(Scheme) ;; With Antti Karttunen's IntSeq-library.

(define A267097 (LEFTINV-LEASTMONO 1 1 A080147))

CROSSREFS

Cf. A000040, A002144, A080147, A267098.

Cf. also A267101.

Sequence in context: A120565 A244989 A296021 * A194198 A189674 A156250

Adjacent sequences: A267094 A267095 A267096 * A267098 A267099 A267100

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 01 2016

STATUS

approved