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Search: id:A128877
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| A128877 |
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Numerator of the continued fraction convergents of the decimal concatenation of the powers of 10. |
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+0
1
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| 0, 1, 12, 109, 121, 10999, 11120, 111079, 122199, 1088671, 5565554, 23350887, 122319989, 1001910799, 1124230788, 11119987891, 112324109698, 123444097589, 1346765085588, 5510504439941, 23388782845352, 28899287285293
(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 10 = 1,10,100,1000,10000,... are concatenated and then preceded by a decimal point to create the fraction N = .110100100010000... 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, 10^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: A155608 A138432 A011999 this_sequence A085797 A016161 A081200
Adjacent sequences: A128874 A128875 A128876 this_sequence A128878 A128879 A128880
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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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