[seqfan] Re: Novel Gray-code-like sequence

[Tom Duff]

It doesn't matter if you're on fresh ground or not. If the sequence is
not in the OEIS, you should submit it.
That said, you probably are on new ground.

On Thu, Nov 5, 2020 at 12:57 PM Allan Wechsler <acwacw at gmail.com> wrote:
>
> I would have just submitted this, but the idea seems so obvious that I
> worried that I would be almost-duplicating an existing concept. So,
> colleagues, I appeal to your collective memories and ask if you have seen
> this before.
>
> The initial entry is 0.
>
> At each step we toggle one bit of the binary representation of the previous
> value.
>
> We always toggle the least significant bit that has never been toggled
> before from this value. Thus, though values will be repeated, pairs of
> values never will.
>
> From 0, the smallest bit that has never been toggled is the 1-bit, so we
> toggle it and arrive at the second entry, 1.
>
> From 1, the smallest bit that has never been toggled is also the 1-bit, so
> we toggle it, taking us back to 0.
>
> From 0, we have toggled the 1-bit before, but never the 2-bit, so we go to
> 2.
>
> If I have made no errors, the sequence begins:
>
> 0,1,0,2,3,2,0,4,5,4,6,7,6,4,0,8,9,8,10,11,10,8,12,13,12,14,15,14,12,8,0,...
>
> After the first seven or eight entries OEIS shrugs. I will submit (and
> write a program and everything) if your collective wisdom assures me I am
> indeed on fresh ground.
>
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