"More"-Cam

[Richard Guy]

For my next act (copied to math-fun as well) I tried
A058631, and found the world's largest partial quotient!

My deep method was to set \precision=1000 in PARI,
then type in cf(0.01101001...), the Thue-Morse
sequence, using C^K and C^Y to copy chunks of sequence.

You can check how far and how correctly I went, but the
results agree as far as the webcam shows.

The immense p.q. occurs somewhere around where I'd
expect the precision to expire, but how did it happen?

? \precision=1000
   precision = 1000 significant digits
? cf(0.0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100101101001100101101001011001101001100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110) 
%19 = [0, 90, 1, 4, 1, 3, 5, 4, 6, 8, 4, 5, 4, 1, 3, 30, 1, 5, 3, 2, 65, 1, 37, 20, 2, 1, 5, 1, 14, 2, 1, 4, 1, 30, 2, 1, 32, 3, 1, 4, 5, 80, 1, 4, 1, 4, 3, 1, 3, 6, 7, 9, 1, 7, 1, 4, 1, 9, 1, 1, 1, 1, 4, 2, 9, 1, 1, 2, 10, 3, 1, 69, 1, 2, 12, 1, 1, 1, 1, 5, 1, 1, 1, 2, 5, 4, 1, 1, 27, 3, 3, 1, 2, 1, 1, 1, 1, 2, 1, 4, 1, 1, 101, 5, 1, 4, 5, 1, 3, 2, 6, 1, 3, 8, 1, 3, 1, 48, 4, 2, 1, 1, 2, 2, 56, 9, 1, 2, 1, 1, 21, 2, 4, 12, 2, 16, 8, 1, 5, 4, 9, 1, 3, 2, 1, 2, 1, 1, 1, 3, 6, 1, 1, 5, 8, 1, 3, 1, 7, 4, 8, 1, 2, 24, 2, 2, 17, 1, 1, 1, 1, 1, 55, 1, 5, 1, 1, 63, 4, 1, 121, 2, 54, 1, 2, 1, 7, 1, 2, 2, 10, 1, 1, 12, 1, 21, 17, 3, 1, 3, 3, 4, 1, 7, 5, 9, 2, 1, 1, 1, 2, 1, 4, 5, 1, 15, 1, 1, 1, 131, 1, 1, 2, 1, 2, 1, 1, 2, 1, 8, 2, 1, 1, 3, 1, 5, 1, 1, 2, 1, 2, 1, 3, 36, 1, 4, 2, 2, 3, 1, 2, 9, 3, 6, 1, 4, 4, 2, 1, 11, 22, 1, 1, 1, 1, 2, 25, 4, 2, 3, 1, 1, 2, 1, 1, 6, 1, 16, 1, 10, 2, 2, 2, 1, 1, 4, 4, 1, 2, 23, 1, 1, 4, 1, 5, 6, 5, 1, 3, 1, 1, 2, 12, 2, 32, 1, 1, 7, 1, 4, 95, 9, 1,!
 28, 2, 12, 1, 2, 2, 1, 6, 1, 4, 2, 1, 1, 3, 1, 2, 2, 1, 1, 13, 1, 4, 8, 1, 1, 15, 3, 2, 2, 1, 1, 11, 7, 1, 2, 1, 12, 1, 1, 2, 12, 1, 58, 3, 2, 2, 195, 1, 1, 8, 1, 3, 10, 2, 2, 1, 1, 6, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 11, 1, 3, 7, 3, 2, 6, 29, 1, 15, 1, 77, 1, 1, 2, 9, 1, 8, 6, 2, 3, 2, 3, 3, 4, 8, 2, 1, 3, 3, 2, 2, 3, 2, 9, 7, 1, 1, 1, 2, 1, 1, 4, 7, 2, 1, 1, 69, 1, 9, 1, 1, 6, 1, 284, 3, 1, 46, 1, 3, 1, 1, 2, 1, 1, 2, 4, 2, 2, 1, 8, 2, 3, 1, 1, 3, 1, 1, 12, 1, 3, 2, 1, 1, 9, 4, 1, 2, 2, 3, 1, 9, 1, 5, 6, 3, 7, 1, 1, 3, 1, 3, 3, 5, 1, 2, 1, 1, 1, 2, 1, 15, 1, 12, 1, 1, 56, 1, 7, 3, 3, 2, 1, 1385736680941098779343511937759072217374568926604871763256745788, 3, 5, 1, 3, 5, 1, 2, 1, 3, 1, 1, 8, 1, 2, 7, 1, 29, 1, 1, 3, 1, 2, 32, 1, 2, 4, 11, 13, 12, 2, 2, 1, 1, 1128, 5, 3, 1, 11, 1, 13, 4, 3, 2, 1, 1, 2, 2, 1, 1, 1, 7, 14, 3, 1, 13, 2, 11, 2, 12, 3, 2, 3, 81, 2, 22, 5, 1, 66, 5, 1332, 1, 8, 5, 1, 1, 11, 4, 16, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 97, 2, 1, 6, 1, 10, 3, 132, 8, 1, !
6, 1, 2, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 2, 16, 11, 1, 23, 1!
0, 2, 1, 
 5, 2, 1, 1, 4, 1, 2, 4, 3, 2, 1, 2, 1, 1, 3, 1, 5, 2, 11, 1, 2, 1, 7, 7, 2, 6, 3, 1, 2, 3, 1, 2, 2, 3, 1, 1, 5, 1, 1, 1, 3, 1, 8, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 8, 1, 2, 1, 57, 2, 1, 7, 2, 1, 6, 1, 1, 13, 1, 36, 1, 5, 1, 5, 8, 1, 3, 1, 3, 1, 1, 1, 4, 16, 10, 18, 1, 3, 1, 2, 45, 2, 5, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 23, 52, 1, 8, 1, 2, 1, 1, 13, 2, 1, 1, 2, 1, 2, 9, 77, 1, 1, 1, 4, 2, 1, 1, 10, 2, 2, 3, 1, 1, 53, 1, 4, 5, 4, 3, 1, 1, 1, 3, 38, 1, 1, 4, 1, 8, 2, 1, 6, 5, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 5, 1, 13, 1, 6, 7, 1, 57, 1, 6, 1, 11, 1, 105, 1, 4, 2, 15, 1, 1, 1, 2, 1, 3, 2, 1, 27, 1, 8, 2, 1, 2, 5, 1, 1, 3, 11, 1, 7, 1, 34, 1, 1, 3, 1, 4, 13, 2, 2, 1, 13, 1, 2, 1, 11, 3, 2]
? 
On Fri, 15 Jun 2001, N. J. A. Sloane wrote:

> Following a suggestion of Frank Ellermann, the WebCam has a fourth 
> button, for browsing the sequences that need extending.
> 
>  Try the new Integer Sequence WebCam at
>     http://www.research.att.com/~njas/sequences/WebCam.html !
>  
>  Neil J. A. Sloane, njas at research.att.com,
>  AT&T Shannon Lab, 180 Park Ave, Room C233,
>  Florham Park, NJ 07932-0971 USA.
>  Home page: http://www.research.att.com/~njas/
>  (or www.research.att.com/%7enjas/ if your keyboard has no tilde)
>  Office: (973) 360 8415; fax: (973) 360 8178; virtual office: (732) 828 6098
>