A128871 Numerator of the continued fraction convergents of the decimal concatenation of the Fibonacci numbers.

0, 1, 890, 24031, 24921, 2017711, 2042632, 4060343, 6102975, 10163318, 26429611, 36592929, 282580114, 884333271, 1166913385, 2051246656, 7320653353, 16692553362, 24013206715, 136758586937, 434288967526, 571047554463

Offset

0,3

Links

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

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

Crossrefs

Sequence in context: A252577 A202528 A006916 * A110726 A204366 A266915

Adjacent sequences: A128868 A128869 A128870 * A128872 A128873 A128874

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 18 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved