A128873 - OEIS

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

%S 0,1,84,85,1444,1529,85539,87068,172607,259675,691957,1643589,

%T 192991870,194635459,776898247,1748431953,9519058012,11267489965,

%U 99658977732,210585445429,8312491349463,16835568144355,25148059493818

%N Numerator of the continued fraction convergents of the decimal concatenation of the powers of 2.

%F The powers of 2 = 1,2,4,8,16,32,64,... are concatenated and then preceded by a decimal point to create the fraction N = .1248163264128... 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,2^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