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 A102613 #7 Aug 31 2024 19:20:49
%S A102613 0,1,2,1,3,1,4,1,4,2,5,5,6,3,2,3,7,7,8,2,8,4,9,3,9,9,1,9,10,1,11,11,1,
%T A102613 11,11,11,12,6,4,3,13,13,14,7,14,7,15,5,15,3,5,15,16,8,16,2,16,8,17,
%U A102613 17,18,9,2,9,18,3,19,19,19,19,20,5,21,21,7,21,3,7,22,11,22,11,23,23,23,23
%N A102613 Numerator of the reduced fractions of the ratios of the number of primes less than n over the number of composites less than n.
%C A102613 Conjecture: The ratio pi(x)/(n-pi(x)) tends to 0 as n tends to infinity. This is evident from the fact that Li(x)/(n-Li(x)) -> 0 as n -> infinity but unfortunately not proof.
%F A102613 a(n) = numerator(pi(n)/(n-pi(n))) = numerator(A000720(n)/A062298(n)). - _Jason Yuen_, Aug 31 2024
%o A102613 (PARI) pixovcmpx(n) = for(x=1,n,print1(numerator(pi(x)/(x-pi(x)))",")) pi(n) = \Number of primes less than or equal to n. { local(c,x); c=0;forprime(x=1,n,c++);return(c) }
%o A102613 (PARI) a(n)=numerator(primepi(n)/(n-primepi(n))) \\ _Jason Yuen_, Aug 31 2024
%Y A102613 Cf. A000720, A062298.
%K A102613 frac,nonn,easy
%O A102613 1,3
%A A102613 _Cino Hilliard_, Jan 30 2005