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Search: id:A128872
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| A128872 |
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Denominator of the continued fraction convergents of the decimal concatenation of the Fibonacci numbers. |
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+0
1
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| 1, 89, 79211, 2138786, 2217997, 179578546, 181796543, 361375089, 543171632, 904546721, 2352265074, 3256811795, 25149947639, 78706654712, 103856602351, 182563257063, 651546373540, 1485656004143, 2137202377683, 12171667892558
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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The Fibonacci numbers 0,1,1,2,3,5,8,13... are concatenated and then preceded by a decimal point to create the fraction N = .01123581321... 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
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PROGRAM
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(PARI) fib(n) = a="."; for(x=0, n, a=concat(a, Str(fibonacci(x)))); a=eval(a) cfrac2(m, 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(denom", "); numer2=numer; denom2=denom; ) }
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CROSSREFS
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Sequence in context: A023330 A059766 A033513 this_sequence A073905 A089158 A136031
Adjacent sequences: A128869 A128870 A128871 this_sequence A128873 A128874 A128875
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KEYWORD
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frac,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)hotmail.com), Apr 18 2007
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