Problem

[Richard Guy]

Yes, we address cubic bracelets also.
I have too much on my plate at present, but
will send the present state of the paper
to Berlekamp quite soon, and we'll endeavor
to make it public in some form.  The
original title was Fibonacci plays billiards.

R.

On Mon, 23 Jan 2006, Roberto Tauraso wrote:

> On Sun, 22 Jan 2006, Richard Guy wrote:
>
>> The square bracelet conjecture is answered
>> in a preprint of Berlekamp & Guy.  We should
>> make this more available.
>
> Really! I'm very happy of that. Is it possible to receive
> an electronic copy of this work?
> In these days I searched in the web but I did not find it.
> Just yesterday I submitted the sequence A115418
> about the minimum lenght of k-th-power loop (or bracelet).
> The sequence is not very long (it starts with index 1):
> 2, 32, 473, 9641
> 32 is well known and 473 was found also by Resta in
> http://www.primepuzzles.net/puzzles/puzz_311.htm
> It would be nice to extend it but for k=5. The first number
> such that all the numbers have degree at least 2 is 246877
> and to find the cycle for such a huge graph is not easy
> (at least for me).
> I wonder if the Berlekamp & Guy result can be extended also
> for cube loops: do cube loops exist from 473 on?
>
> Bye,
> Roberto Tauraso
>
>