OFFSET
1,1
COMMENTS
This will be a very long but finite sequence, since pi(x)/li(x) will exceed unity for some very large values of x (as Littlewood first showed) but then will asymptotically tend to unity by the prime number theorem. One large but unknown element of the sequence will be the smallest x for which pi(x)>li(x).
EXAMPLE
For 1.5<x<2, li(x)>0 and pi(x)=0, so pi(x)/li(x)=0. a(1)=2 because at x=2, pi(x)/li(x) has its increase, to 1/li(2)=0.9567878442. a(2)=1051 because x=1051 gives the next time pi(x)/li(x) gives a higher value, 177/Li(1051)=0.956932676.
MAPLE
with(numtheory): Digits:=50; s:=0: for n from 1 to 10000 do if (evalf(n/Li(ithprime(n)))>s) then s:=evalf(n/Li(ithprime(n))): print(ithprime(n)) else s:=s end if end do;
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Don N. Page, Oct 24 2005
STATUS
approved