login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 0

%I

%S 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 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 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 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 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 pi(n) is the number of primes <= n. Number of composites <= n = n - pi(n).

%o (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) }

%K frac,nonn

%O 1,3

%A _Cino Hilliard_, Jan 30 2005

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 1 20:42 EST 2023. Contains 359995 sequences. (Running on oeis4.)