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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

Table of n, a(n) for n=0..12.

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.)