A128839 - OEIS

%I #4 Oct 01 2013 21:35:21

%S 1,2,3,8,11,140,151,442,1477,1919,11072,12991,24063,37054,98171,

%T 429738,957647,6175620,13308887

%N Numerators of the continued fraction convergents of the decimal concatenation of the odd natural numbers.

%C The 19th convergent breaks down at number 95 so a 16 digit ratio gives 91 digits accuracy!

%F The odd natural numbers 1,3,5.. are concatenated and then preceded by a decimal point to create the fraction N = .1357911131517... . This number is then evaluated with n=1,m=steps to iterate,x = N, a(0)=floor(N) using the loop: do a(n)=floor(x) x=1/(x-a(n)) n=n+1 loop until n=m

%e The 19th convergent 13308887/98010000 =

%e 0.13579111315171921232527293133353739414345474951535557596163656769717375777981\

%e 8385878991939598000...

%o (PARI) catodd(n) = f=".";forstep(x=1,n,2,a=concat(f,Str(x)));f=eval(f) cfrac2(m,f) = { default(realprecision,1000); cf = vector(m+10); cf = contfrac(f); for(m1=1,m-1, r=cf[m1+1]; forstep(n=m1,1,-1, r = 1/r; r+=cf[n];); numer=numerator(r); denom=denominator(r); print1(numer","); ) }

%K frac,nonn,base

%O 1,2

%A _Cino Hilliard_, Apr 16 2007

%E Edited by _Charles R Greathouse IV_, Apr 25 2010