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Search: id:A128842
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| A128842 |
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Numerators of the continued fraction convergents of the decimal concatenation of the even natural numbers. |
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+0
1
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| 1, 1, 2, 29, 118, 265, 648, 913, 20734, 21647, 388733, 410380, 1209493
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The 15 digit ratio of the 13th convergent gives an accuracy of 93 digits in the expansion.
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FORMULA
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The even natural numbers 0,2,4.. are concatenated and then preceded by a decimal point to create the fraction N = .024681012... . 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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EXAMPLE
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The 13th convergent 1209493/49005000 =
0.02468101214161820222426283032343638404244464850525456586062646668707274767880\
8284868890929496990...
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PROGRAM
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(PARI) cateven(n) = f="."; forstep(x=0, 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: A141949 A123004 A062618 this_sequence A028883 A024200 A132412
Adjacent sequences: A128839 A128840 A128841 this_sequence A128843 A128844 A128845
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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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