[seqfan] Re: plastic number base

[Alonso Del Arte]

I'm guessing 1 would just be 1. How would 2 be represented? Would the
length of 2's representation be typical for small integers up to about 10^4?

Al

On Tue, Jul 9, 2013 at 4:31 AM, Dale Gerdemann <dale.gerdemann at gmail.com>wrote:

> Hello Seqfans,
>
>
> Suppose we represent numbers in "plastic number base" (like golden ratio
> base  but using the plastic number instead of the golden ratio). There are
> some numbers that are expressed using a surprisingly small number of terms.
> For example, 10717 requires the following powers of the plastic number:
> [33, -18, -42, -47, -53, -67]. Here's  a  small list of examplesL:
>
>
> 10717  [33, -18, -42, -47, -53, -67]
> 12214  [33, 26, -11, -19, -29, -42, -67]
> 14197  [34, -19, -24, -33, -42, -47, -54, -67]
> 24914  [36, -16, -24, -33, -39, -47, -65, -72]
> 57918  [39, -19, -26, -31, -37, -49, -54, -60, -68, -74, -80]
> 101639 [41, -19, -28, -34, -51, -64, -72, -80]
> 115836 [41, 34, -16, -31, -41, -54, -63, -70, -76, -85]
> 192561 [43, 34, -20, -27, -42, -48, -58, -67, -75, -85]
> 236282 [44, -20, -33, -42, -51, -57, -62, -80, -85]
> 370925 [45, 39, -22, -32, -42, -50, -59, -73, -79, -87, -93]
> 414646 [46, -23, -30, -42, -57, -74, -87, -93]
>
> Is there any signicance to these numbers?
>
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Alonso del Arte
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