A366134 - OEIS

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

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OFFSET

1,12

COMMENTS

Inspired by A365573.

LINKS

Table of n, a(n) for n=1..95.

FORMULA

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

MATHEMATICA

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

PROG