A365573 Number of primes between prime(n) and prime(n)+log(prime(n)), exclusive.

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

Offset: 1

Author

Alain Rocchelli, Sep 09 2023

Keywords

• nonn

Comments

Inspired by A354841.

Crossrefs

Cf. A068985, A354841, A275235.

Programs

PARI

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

Formula

Conjecture: Limit_{N->oo} (Ratio_{n=1..N} a(n)=0) = 1/e (A068985).