Re: Fibonacci[1,000,000,000] contains 208,987,640 decimal digits

From: Fred the Wonder Worm (ftww_at_maths.usyd.edu.au)
Date: 08/11/04 

Date: 11 Aug 2004 01:18:48 GMT

In article <cf9fus$hs2$1@spacebar.ucc.usyd.edu.au>,
Fred the Wonder Worm <ftww@maths.usyd.edu.au> wrote:
>
> [...] The version I would use (for n > 0) is:
>
> Ceiling(n*Log[10](phi) - Log[10](Sqrt(5)))
>
> where phi = (1 + Sqrt(5))/2.

[...]

>> N. Sloane get now a comment to A068070 with the corrected sequence
>> {0,2,21,209,2090,20899,208988,2089877,20898764,208987640,2089876402,
>> 20898764025,208987640250,2089876402500,20898764024998,208987640249979,
>> 2089876402499787,20898764024997873,208987640249978734,...}.
>
> The first value is clearly not correct -- the formula does not work
> for n = 0 as the contribution from 1/phi^n in the usual formula is
> not negligible. Your values for n = 10 and n = 17 are also incorrect;
> they should be 2089876403 and 20898764024997874 respectively. The
> others are correct.
>
> [ The current data in the online encyclopaedia as I write this is
> wrong for n = 8, 9 and 16. ]

A slight correction to my post. I have used 'n' with two different
meanings, right next to each other even. :( In the formula and the
1/phi^n comment it is intended to refer to the index of the Fibonacci
number being computed; the other uses were for the sequence index,
where n corresponds to the 10^n th Fibonacci number (and thus 10^n
in the formula).

My apologies for such sloppiness and any confusion this causes.

Cheers,
Geoff.

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Geoff Bailey (Fred the Wonder Worm) | Programmer by trade --
ftww@maths.usyd.edu.au | Gameplayer by vocation.
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