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A128843 Denominators of the continued fraction convergents of the decimal concatenation of the even natural numbers. 0
40, 41, 81, 1175, 4781, 10737, 26255, 36992, 840079, 877071, 15750286, 16627357, 49005000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The 15 digit ratio of the 13th convergent gives an accuracy of 93 digits in the expansion.
LINKS
FORMULA
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
EXAMPLE
The 13th convergent 1209493/49005000 =
0.02468101214161820222426283032343638404244464850525456586062646668707274767880\
8284868890929496990...
PROG
(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(denom", "); ) }
CROSSREFS
Sequence in context: A082763 A007634 A228184 * A214563 A111167 A070980
KEYWORD
frac,nonn,base
AUTHOR
Cino Hilliard, Apr 16 2007
EXTENSIONS
Edited by Charles R Greathouse IV, Apr 25 2010
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)