OFFSET
0,1
COMMENTS
The 15 digit ratio of the 13th convergent gives an accuracy of 93 digits in the expansion.
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
KEYWORD
frac,nonn,base
AUTHOR
Cino Hilliard, Apr 16 2007
EXTENSIONS
Edited by Charles R Greathouse IV, Apr 25 2010
STATUS
approved