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Number of primes between prime(n) and prime(n)+log(prime(n)), exclusive.
1

%I #6 Sep 27 2023 13:43:32

%S 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,

%T 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,

%U 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

%N Number of primes between prime(n) and prime(n)+log(prime(n)), exclusive.

%C Inspired by A354841.

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

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

%Y Cf. A068985, A354841, A275235.

%K nonn

%O 1,88

%A _Alain Rocchelli_, Sep 09 2023