Search: id:A128838
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%I A128838
%S A128838 1,81,120758446,241516973,1328343311,2898203595,4226546906,49390219561,
%T A128838 53616766467,103006986028,156623752495,886125748503,1042749500998,
%U A128838 1928875249501,2971624750499,4900500000000
%N A128838 Denomonators of the continued fraction convergents of the decimal concatenation 
               of the natural numbers.
%C A128838 The 15th convergent breaks down at number 16 so a 24 digit ratio gives 
               24 digits accuracy. The 16th convergent breaks down at the 97th number. 
               It is amazing that a 24 digit ratio gives 186 digits of accuracy 
               in the expansion!
%F A128838 The natural numbers 0,1,2,3,.. are concatenated and then preceded by 
               a decimal point to create the fraction N = .0123456789101112131415... 
               . 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 A128838 The 15th convergent
%e A128838 36686725011/2971624750499 = 0.01234567891011121314151610314942472616...
%e A128838 The 16th convergent 60499999499/4900500000000 =
%e A128838 0.0123456789101112131415161718192021222324252627282930313233343536373839404142\
%e A128838 434445464748495051525354555657585960616263646566676869707172737475767778798081\
%e A128838 8283848586878889909192939495969799000...
%o A128838 (PARI) cfrac2(m,f) = { default(realprecision,1000); cf = vector(m+10); 
               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(denom",
               "); ) }
%Y A128838 Sequence in context: A092258 A162284 A116268 this_sequence A051001 A033402 
               A143757
%Y A128838 Adjacent sequences: A128835 A128836 A128837 this_sequence A128839 A128840 
               A128841
%K A128838 frac,nonn
%O A128838 0,2
%A A128838 Cino Hilliard (hillcino368(AT)hotmail.com), Apr 15 2007

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