A128872 Denominator of the continued fraction convergents of the decimal concatenation of the Fibonacci numbers.

1, 89, 79211, 2138786, 2217997, 179578546, 181796543, 361375089, 543171632, 904546721, 2352265074, 3256811795, 25149947639, 78706654712, 103856602351, 182563257063, 651546373540, 1485656004143, 2137202377683, 12171667892558

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

The Fibonacci numbers 0,1,1,2,3,5,8,13... are concatenated and then preceded by a decimal point to create the fraction N = .01123581321... 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) fib(n) = a="."; for(x=0, n, a=concat(a, Str(fibonacci(x)))); a=eval(a) cfrac2(m, 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: A023330 A059766 A033513 * A263379 A073905 A089158

Adjacent sequences: A128869 A128870 A128871 * A128873 A128874 A128875

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 18 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved