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A128877 Numerator of the continued fraction convergents of the decimal concatenation of the powers of 10. 0
0, 1, 12, 109, 121, 10999, 11120, 111079, 122199, 1088671, 5565554, 23350887, 122319989, 1001910799, 1124230788, 11119987891, 112324109698, 123444097589, 1346765085588, 5510504439941, 23388782845352, 28899287285293 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

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(numer", "); numer2=numer; denom2=denom; ) }

CROSSREFS

Sequence in context: A289291 A138432 A011999 * A085797 A016161 A081200

Adjacent sequences:  A128874 A128875 A128876 * A128878 A128879 A128880

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 January 28 15:13 EST 2022. Contains 350656 sequences. (Running on oeis4.)