A128877 Numerator of the continued fraction convergents of the decimal concatenation of the powers of 10.

0, 1, 12, 109, 121, 10999, 11120, 111079, 122199, 1088671, 5565554, 23350887, 122319989, 1001910799, 1124230788, 11119987891, 112324109698, 123444097589, 1346765085588, 5510504439941, 23388782845352, 28899287285293

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