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

1,88

Comments

Inspired by A354841.

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A068985, A354841, A275235.

Sequence in context: A350797 A283988 A276204 * A370278 A369245 A353310

Adjacent sequences: A365570 A365571 A365572 * A365574 A365575 A365576

Keyword

nonn

Author

Alain Rocchelli, Sep 09 2023

Status

approved