%I A128842
%S A128842 1,1,2,29,118,265,648,913,20734,21647,388733,410380,1209493
%N A128842 Numerators of the continued fraction convergents of the decimal concatenation 
               of the even natural numbers.
%C A128842 The 15 digit ratio of the 13th convergent gives an accuracy of 93 digits 
               in the expansion.
%F A128842 The even natural numbers 0,2,4.. are concatenated and then preceded by 
               a decimal point to create the fraction N = .024681012... . 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
%e A128842 The 13th convergent 1209493/49005000 =
%e A128842 0.02468101214161820222426283032343638404244464850525456586062646668707274767880\
%e A128842 8284868890929496990...
%o A128842 (PARI) cateven(n) = f=".";forstep(x=0,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",
               "); ) }
%Y A128842 Sequence in context: A141949 A123004 A062618 this_sequence A028883 A024200 
               A132412
%Y A128842 Adjacent sequences: A128839 A128840 A128841 this_sequence A128843 A128844 
               A128845
%K A128842 frac,nonn
%O A128842 0,3
%A A128842 Cino Hilliard (hillcino368(AT)hotmail.com), Apr 16 2007