[seqfan] Re: A030287 et al minor inconsistency

[M. F. Hasler]

On Wed, Nov 8, 2017 at 3:31 AM, Ray Chandler <rayjchandler at sbcglobal.net>
wrote:

> A030287-A030290 are simply lists and should have offset 1.
>

That might be argued about for
A030287 = Digits of a(n)^2 do not appear in a(n-1)^2.

This definition isn't complete without specifying the initial term,
and should also say "least number > a(n-1) such that...",
since else you could take a smaller number
[possibly the smallest unused one, which would perfectly make sense,
the corresponding sequence without squares already exists:
A067581 a(n) = smallest integer not yet in the sequence with no digits in
common with a(n-1), a(0)=0.
].

So, rather than a list, it is a recurrent sequence a(n) = f( a(n-1) ).
And it is not unnatural that the initial term has index 0.
as is the case for most recurrent sequences.

The fact that this implies a(n) = n for n = 0..7 is another motivation.
Another motivation is the fact that restriction to n=1..oo gives you the
"...positive integer..." version, as compared to the current "nonnegative
integer" version.

- Maximilian
on behalf of the Committee for the defense of 0-indexed sequences ;-)



> > -----Original Message-----
> > From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of David
> > Wilson
> > Sent: Tuesday, November 7, 2017 10:39 PM
> > To: 'Sequence Fanatics Discussion list' <seqfan at list.seqfan.eu>
> > Subject: [seqfan] A030287 et al minor inconsistency
> >
> > I'm planning on bringing some consistency to A030287 through A030290, and
> > to extend their b-files.
> > A030287 and A030288 start with a(0) =0, A03028 9 and A030290 with a(1) =
> 0, I
> > think all should have the same start index, I prefer 0, what think ye?
> > It would be nice to agree on indexing before I update any b-files.
> >
> > We also have the weird
> >
> > A030287(n)^2 = A030288(n)  (square elements to get the next sequence)
> > A030290(n)^3 = A030289(n)  (cube elements to get the previous sequence)
>