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Search: id:A128839
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| A128839 |
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Numerators of the continued fraction convergents of the decimal concatenation of the odd natural numbers. |
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+0
1
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| 1, 2, 3, 8, 11, 140, 151, 442, 1477, 1919, 11072, 12991, 24063, 37054, 98171, 429738, 957647, 6175620, 13308887
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The 19th convergent breaks down at number 95 so a 16 digit ratio gives 91 digits accuracy!
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FORMULA
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The odd natural numbers 1,3,5.. are concatenated and then preceded by a decimal point to create the fraction N = .1357911131517... . This number is then evaluated with n=1,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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EXAMPLE
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The 19th convergent 13308887/98010000 =
0.13579111315171921232527293133353739414345474951535557596163656769717375777981\
8385878991939598000...
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PROGRAM
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(PARI) catodd(n) = f="."; forstep(x=1, 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", "); ) }
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CROSSREFS
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Sequence in context: A139447 A042783 A042583 this_sequence A164817 A002958 A115449
Adjacent sequences: A128836 A128837 A128838 this_sequence A128840 A128841 A128842
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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 16 2007
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