cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A192227 Number of primes in the range (n - 2*sqrt(sqrt(n)), n].

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%I A192227 #16 Feb 27 2019 01:18:19
%S A192227 0,1,2,2,2,2,2,2,1,1,1,1,2,2,1,1,2,1,2,2,2,1,2,1,1,1,1,0,1,1,2,2,2,1,
%T A192227 1,0,1,1,1,1,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,
%U A192227 1,1,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,1
%N A192227 Number of primes in the range (n - 2*sqrt(sqrt(n)), n].
%C A192227 a(n) is probably positive for all n > 191913030. - _Charles R Greathouse IV_, Jul 01 2011
%F A192227 Conjecturally, a(n) ~ 2*n^(1/4)/log n. - _Charles R Greathouse IV_, Jul 01 2011
%p A192227 A192227 := proc(n) local nhi, nlo ; nhi := n ; nlo := floor( n-2*root[4](n)) ; numtheory[pi](nhi)-numtheory[pi](nlo) ; end proc; # _R. J. Mathar_, Jul 12 2011
%t A192227 Table[PrimePi[n]-PrimePi[n-2*Sqrt[Sqrt[n]]],{n,90}] (* _Harvey P. Dale_, Feb 24 2018 *)
%Y A192227 Cf. A188817, A189025, A192226.
%K A192227 nonn
%O A192227 1,3
%A A192227 _Juri-Stepan Gerasimov_, Jun 26 2011