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Search: id:A128873
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| A128873 |
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Numerator of the continued fraction convergents of the decimal concatenation of the powers of 2. |
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+0
1
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| 0, 1, 84, 85, 1444, 1529, 85539, 87068, 172607, 259675, 691957, 1643589, 192991870, 194635459, 776898247, 1748431953, 9519058012, 11267489965, 99658977732, 210585445429, 8312491349463, 16835568144355, 25148059493818
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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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
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PROGRAM
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(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; ) }
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CROSSREFS
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Sequence in context: A066689 A008898 A033404 this_sequence A095607 A068405 A045569
Adjacent sequences: A128870 A128871 A128872 this_sequence A128874 A128875 A128876
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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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