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

[Rémy Etc]

>> 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,..

Apparently, A215020(n) gives the bit to toggle at n-th step.

best regards,

Rémy Sigrist

Le jeu. 5 nov. 2020 à 19:22, Tom Duff <td at pixar.com> a écrit :

> 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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>
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