[seqfan] Re: A possible characterization of A125121

[William Keith]

On Sat, Nov 16, 2013 at 6:22 PM, Allan Wechsler <acwacw at gmail.com> wrote:

> I think I am having a terminology difference with David Wilson. I intended
> my "tilings" to cover all the integers, not just the non-negative ones, and
> thus right shifts are not only allowed, they are necessary.
>
> This also explains our difference of opinion about 35.  I agree 100011
> can't tile just the non-negative integers, but it *can* tile all the
> integers, as I thought I showed in a previous message.
>

More importantly, don't you also need flips, which don't correspond to
multiplications?

100011
0100011 would collide

100011
00100011
-------------
10101111 but now what do you do about those two single 0s?  You can cover
them if you take

110001
00110001
0000100011
000000100011
--------------------
111111111111 and now you can tile the integers.

But reversal is not a simple arithmetic operation.

William Keith