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%I #4 Oct 01 2013 21:35:21
%S 0,1,12,109,121,10999,11120,111079,122199,1088671,5565554,23350887,
%T 122319989,1001910799,1124230788,11119987891,112324109698,
%U 123444097589,1346765085588,5510504439941,23388782845352,28899287285293
%N Numerator of the continued fraction convergents of the decimal concatenation of the powers of 10.
%F The powers of 10 = 1,10,100,1000,10000,... are concatenated and then preceded by a decimal point to create the fraction N = .110100100010000... This number is then evaluated with n=0,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
%o (PARI) g(n) = f=".";for(x=0,n,a=concat(f,10^x));f=eval(f) { default(realprecision,1000); cf = vector(1000); cf = contfrac(f); for(m1=0,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","); numer2=numer;denom2=denom; ) }
%K frac,nonn,base
%O 0,3
%A _Cino Hilliard_, Apr 18 2007
%E Edited by _Charles R Greathouse IV_, Apr 25 2010
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