Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Oct 23 2023 01:44:39
%S 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,
%T 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,
%U 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
%N Number of primes between prime(n) and prime(n)+2*log(prime(n)), exclusive.
%C Inspired by A365573.
%F Conjecture: Limit_{N->oo} (Ratio_{n=1..N} a(n)=0) = 1/e^2 (A092553).
%t a[n_]:=PrimePi[Prime[n]+2Log[Prime[n]]]-PrimePi[Prime[n]]; Array[a,95] (* _Stefano Spezia_, Sep 30 2023 *)
%o (PARI) a(n) = primepi(prime(n)+2*log(prime(n))) - primepi(prime(n))
%Y Cf. A365573, A354841, A092553.
%K nonn
%O 1,12
%A _Alain Rocchelli_, Sep 30 2023