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A128876 Denominator of the continued fraction convergents of the decimal concatenation of the powers of 10. 0
1, 9, 109, 990, 1099, 99900, 100999, 1008891, 1109890, 9888011, 50549945, 212087791, 1110988900, 9099998991, 10210987891, 100998890010, 1020199887991, 1121198778001, 12232187668001, 50049949450005, 212431985468021 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

The powers of 10 = 1,10,100,1000,10000,... are concatenated and then preceded by a decimal point to create the fraction N = .110100100010000... 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

PROG

(PARI) g(n) = f="."; for(x=0, n, a=concat(f, 10^x)); f=eval(f) { default(realprecision, 1000); cf = vector(1000); cf = contfrac(f); for(m1=0, 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", "); numer2=numer; denom2=denom; ) }

CROSSREFS

Sequence in context: A166846 A058421 A267795 * A199030 A288692 A291815

Adjacent sequences:  A128873 A128874 A128875 * A128877 A128878 A128879

KEYWORD

frac,nonn,base

AUTHOR

Cino Hilliard, Apr 18 2007

EXTENSIONS

Edited by Charles R Greathouse IV, Apr 25 2010

STATUS

approved

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Last modified July 30 10:09 EDT 2021. Contains 346359 sequences. (Running on oeis4.)