A364459 Number of primes in the interval [n,n+log(n)^2].

0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 4, 4, 3, 3, 2, 3, 3, 4, 3, 3, 3, 3, 4, 4, 3, 4, 4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 5, 5, 4, 4, 4, 5, 4, 4, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5

Offset: 1

Author

Alain Rocchelli, Jul 25 2023

Keywords

• nonn

Comments

On average, there are log(n) primes in the interval [n,n+log(n)^2] for any number n.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000720, A120936.

Programs

Maple

a:= n-> add(`if`(isprime(i), 1, 0), i=n..floor(n+log(n)^2)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 25 2023

PARI

for(n=2, 100, An=primepi(n+(log(n))^2)-primepi(n-1); print1(An,", "))