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 A240592 #15 Apr 17 2014 03:57:48
%S A240592 1,2,0,2,0,1,1,1,0,0,1,0,1,1,1,1,0,0,2,0,0,1,0,2,0,0,1,1,0,0,1,0,0,0,
%T A240592 2,1,0,2,0,1,0,0,0,0,0,1,0,1,0,1,1,0,0,0,0,2,0,1,0,0,1,0,1,1,0,0,2,0,
%U A240592 0,0,0,0,2,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0
%N A240592 Number of primes between successive composite squarefree numbers (A120944).
%C A240592 First positions where the numbers n=2..5 occur are at: 2, 142, 2180230, 256857823. - _Vaclav Kotesovec_, Apr 17 2014
%e A240592 a(4) is 2 because A120944(4)=15, A120944(5)=21, 2 primes between them: 17 and 19.
%o A240592 (PARI)
%o A240592 freesqrcomp(n)=issquarefree(n)&&!isprime(n)
%o A240592 nextfqc(n)={local(k);k=n+1;while(!freesqrcomp(k),k+=1);return(k)}
%o A240592 primesin(a,b)={local(p=a,q=0);while(p<b,p=nextprime(p);if(p<b,q+=1);p+=1);return(q)}
%o A240592 {for(i=2,1000,if(freesqrcomp(i),m=nextfqc(i);p=primesin(i,m);print(p)))}
%Y A240592 Cf. A120944, A240593.
%K A240592 nonn
%O A240592 1,2
%A A240592 _Antonio Roldán_, Apr 08 2014