A364459 - OEIS

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

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OFFSET

1,5

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

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

PROG

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