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%I #14 Aug 30 2023 14:13:55
%S 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,
%T 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,
%U 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
%N Number of primes in the interval [n,n+log(n)^2].
%C On average, there are log(n) primes in the interval [n,n+log(n)^2] for any number n.
%H Robert Israel, <a href="/A364459/b364459.txt">Table of n, a(n) for n = 1..10000</a>
%p a:= n-> add(`if`(isprime(i), 1, 0), i=n..floor(n+log(n)^2)):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Jul 25 2023
%o (PARI) for(n=2, 100, An=primepi(n+(log(n))^2)-primepi(n-1); print1(An,", "))
%Y Cf. A000040, A000720, A120936.
%K nonn
%O 1,5
%A _Alain Rocchelli_, Jul 25 2023
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