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.
%I A192394 #18 Feb 10 2025 17:44:57
%S A192394 0,1,1,1,1,2,1,2,2,2,3,2,1,2,2,3,2,2,2,2,2,4,4,4,1,2,2,2,4,6,3,4,5,5,
%T A192394 4,4,5,2,3,4,3,4,4,6,6,7,7,3,2,2,3,4,4,5,4,4,2,3,4,4,6,8,5,6,7,7,5,4,
%U A192394 5,5,6,5,5,5,8
%N A192394 Number of semiprimes in the range (prime(n), prime(n)+sqrt(prime(n))).
%H A192394 Harvey P. Dale, <a href="/A192394/b192394.txt">Table of n, a(n) for n = 1..1000</a>
%e A192394 a(1)=0 because there are no semiprimes in the range (2, 2+sqrt(2));
%e A192394 a(2)=1 because there is one semiprime (4) in the range (3, 3+sqrt(3)).
%p A192394 A192394 := proc(n) local a,p,s; a := 0 ; p := ithprime(n) ; for s from p to floor( p+sqrt(p)) do if isA001358(s) then a := a+1 ; end if; end do: a; end proc: # _R. J. Mathar_, Jul 01 2011
%t A192394 (* First run A072000 to define semiPrimePi *) Table[semiPrimePi[Prime[n] + Sqrt[Prime[n]]] - semiPrimePi[Prime[n]], {n, 75}] (* _Alonso del Arte_, Jul 01 2011 *)
%t A192394 Table[Count[Range[p,p+Sqrt[p]],_?(PrimeOmega[#]==2&)],{p,Prime[Range[80]]}] (* _Harvey P. Dale_, Feb 10 2025 *)
%Y A192394 Cf. A001358.
%K A192394 nonn
%O A192394 1,6
%A A192394 _Juri-Stepan Gerasimov_, Jun 29 2011
%E A192394 Corrected by _R. J. Mathar_, Jul 01 2011