A366134 Number of primes between prime(n) and prime(n)+2*log(prime(n)), exclusive.

1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 3, 2, 2, 1, 0, 1, 2, 1, 0, 2, 1, 2, 2, 1, 2, 1, 1, 3, 2, 1, 0, 0, 3, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 3, 2, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 3, 2, 2, 1, 2, 3, 2, 1, 1, 2, 2, 2, 2

Offset: 1

Author

Alain Rocchelli, Sep 30 2023

Keywords

• nonn

Comments

Inspired by A365573.

Crossrefs

Cf. A365573, A354841, A092553.

Programs

Mathematica

a[n_]:=PrimePi[Prime[n]+2Log[Prime[n]]]-PrimePi[Prime[n]]; Array[a,95] (* Stefano Spezia, Sep 30 2023 *)

PARI

a(n) = primepi(prime(n)+2*log(prime(n))) - primepi(prime(n))

Formula

Conjecture: Limit_{N->oo} (Ratio_{n=1..N} a(n)=0) = 1/e^2 (A092553).