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

1,12

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

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

Crossrefs

Cf. A365573, A354841, A092553.

Sequence in context: A337763 A109072 A100727 * A064892 A236344 A333124

Adjacent sequences: A366131 A366132 A366133 * A366135 A366136 A366137

Keyword

nonn

Author

Alain Rocchelli, Sep 30 2023

Status

approved