[seqfan] Re: A168237 startup and offset

[Ali Sada]

 Would it be useful to define sequences like A168237 using a function R(f1(m),f2(m)) where f1(m) is repeated f2(m) times? Both f1(m) and f2(m) can be a constant or a polynomial. f1(m) can even be a sequence itself. 
For example,  the new version of A168237 would become R(3m,2), starting at m = 0.  
A(002024) would become R(m,m), starting at m = 1. 

We can continue with finding the partial sum of R(f1(m),f2(m)) or by applying basic arithmetic operations between different R's. It could be really interesting to find clever formulas to represent such combinations. 

Best,
Ali

    On Tuesday, February 2, 2021, 11:15:28 PM EST, Allan Wechsler <acwacw at gmail.com> wrote:  
 
 Glad to update the b-file; I will try to do that tonight. Somebody still
needs to edit the programs, though.

On Tue, Feb 2, 2021, 12:23 PM Neil Sloane <njasloane at gmail.com> wrote:

> Allan, excellent suggestion. I added a(0)=0. Can you upload a new b-file?
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
>
> On Tue, Feb 2, 2021 at 12:32 AM Allan Wechsler <acwacw at gmail.com> wrote:
>
> > A168237 is the sequence 0,3,3,6,6,9,9,...
> >
> > Its offset is 1.
> >
> > It has a clever formula as definition, which boils down the multiples of
> 3
> > repeated, except for 0 which is only stated once.
> >
> > Can anybody think of a good reason *not* to enhance it by adding A(0) =
> 0,
> > and changing the offset to 0? The clever formula still works, and I think
> > all the comments are still true. (I am slightly unsure of the E.g.f.) The
> > programs would have to be altered slightly, by somebody who knows
> > Mathematica and Magma, but surely the modification would be trivial.
> >
> > All old searches would still match. And I think the resulting sequence
> > would be strictly simpler than what's there now. So that's why I'm asking
> > if I'm missing something.
> >
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> >
>
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