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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 Adjacent sequences:  A128840 A128841 A128842 * A128844 A128845 A128846 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 September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)