[seqfan] Re: A030287 et al minor inconsistency

[David Wilson]

I agree with all of MFH’s arguments that we should have a(0) = 0 in these sequences.

This convention makes it easy to include or exclude the initial 0 by choosing staring index 0 or 1.

Having programmed both older FORTRAN (1-based arrays) and C/C++ (0-based arrays), I am well-acquainted with the joys of 0-based indexing.

However, I think NJAS is a romantic who likes to index starting at 1.

 

From: maximilian at hasler.fr [mailto:maximilian at hasler.fr] On Behalf Of M. F. Hasler
Sent: Wednesday, November 08, 2017 1:44 PM
To: Ray Chandler
Cc: Sequence Fanatics Discussion list; David Wilson
Subject: Re: [seqfan] Re: A030287 et al minor inconsistency

 

 

 

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)