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Number of primes between n and n+log(n), exclusive.
3

%I #17 Jun 27 2022 10:02:56

%S 0,0,0,1,0,1,0,0,1,1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,1,2,1,1,0,0,0,1,

%T 1,1,0,1,1,2,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,2,2,1,1,0,0,1,1,1,1,1,1,

%U 2,2,1,1,0,0,1,1,1,1,1,1,1,1,0,0,1,1,1

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

%C Inspired by A275235.

%t a[n_] := Count[Range[n + 1, n + Log[n]], _?PrimeQ]; Array[a, 100] (* _Amiram Eldar_, Jun 08 2022 *)

%o (PARI) a(n) = primepi(n+log(n)) - primepi(n); \\ _Michel Marcus_, Jun 25 2022

%Y Cf. A275235 (similar, but with n+log(n)^2), A354842.

%K nonn

%O 1,28

%A _Bernard Schott_, Jun 08 2022