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 A128871 Numerator of the continued fraction convergents of the decimal concatenation of the Fibonacci numbers. 0
 0, 1, 890, 24031, 24921, 2017711, 2042632, 4060343, 6102975, 10163318, 26429611, 36592929, 282580114, 884333271, 1166913385, 2051246656, 7320653353, 16692553362, 24013206715, 136758586937, 434288967526, 571047554463 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 15 19:07 EDT 2024. Contains 375173 sequences. (Running on oeis4.)