Don't restrict OEIS sequence domains!

[zak seidov]

David, 

I simply remember Neil's recommendation
(somewhere in his tip's) to omit trivial cases
e.g. if each second term is zero.

And you may wish to 
put in %C A053699 
some of your observations, 
e.g., a(n_odd)=2.
Zak

--- David Wilson <davidwwilson at comcast.net> wrote:

> ----- Original Message ----- 
> From: "zak seidov" <zakseidov at yahoo.com>
> To: <seqfan at ext.jussieu.fr>
> Sent: Sunday, November 05, 2006 1:28 AM
> Subject: Re: Observation on A053669
> 
> 
> > Yes,
> > and because a(n_odd)=2
> > keep only even n's.
> > Zak
> 
> > [Earlier included message elided]
> ---------------------------
> 
> Let's take a look at Zak's recommendation to
> restrict the domain of A053699 
> to even n:
> 
> A053699(n) currently looks like:
> 
>
2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,...
> 
> But a(k) = 2 for odd k, these values are
> uninteresting, so list only a(2n):
> 
>
3,3,5,3,3,5,3,3,5,3,3,5,3,3,7,3,3,5,3,3,5,3,3,5,3,3,5,3,3,7,3,3,5,3,3,5,...
> 
> But now a(k) = 3 unless 6 divides k, so we should
> list only a(6n):
> 
>
5,5,5,5,7,5,5,5,5,7,5,5,5,5,7,5,5,5,5,7,5,5,5,5,7,5,5,5,5,7,5,5,5,5,11,..
> 
> But again, a(k) = 5 except when 30 divides k, so
> let's eject these boring 
> values and keep only a(30n):
> 
>
7,7,7,7,7,7,11,7,7,7,7,7,7,11,7,7,7,7,7,7,11,7,7,7,7,7,7,11,7,7,7,7,7,...
> 
> But look at all the uninteresting 7's. Maybe we
> should list only a(210n)...
> 
> I think you get the picture. In the case of this
> sequence, we repeatedly 
> eliminate uninteresting domain values, but we never
> flush out the elusive 
> "interesting domain" of the sequence. Indeed, we can
> eliminate the entire 
> domain as uninteresting, whereas I think the
> original sequence is indeed 
> quite interesting.
> 
> Clearly, there are times when restricted domains are
> useful. For example, 
> since the areas of Pythagorean triangles are always
> divisible by 6, it would 
> seem reasonable, in the name of compactness, to
> prefer "Number of 
> Pythagorean triangles with area 6n" over "Number of
> Pythagorean triangles of 
> area n", since the latter would have a(n) = 0 for n
> != 6k. Nevertheless, I 
> would advocate having both sequences in the OEIS,
> because we never know if 
> the user will be searching for the compact or
> inflated version of the 
> sequence.
> 
> Similarly, if we adopt Zak's recommendation to
> restrict A065577 to a domain 
> of even values, and then someone looks up
> 
> 2,3,2,3,2,5,2,3,2,3,2,5
> 
> they will probably miss the most straightforward
> explanation of their 
> sequence.
> 
> In short: Don't restrict domains of OEIS sequences
> unless it makes clear 
> sense to do so, and if you do include a sequence on
> some restricted 
> "interesting" domain, have pity on the OEIS users
> and also include the same 
> sequence on its fullest possible domain.
> 
> ----- Original Message ----- 
> From: "zak seidov" <zakseidov at yahoo.com>
> To: <seqfan at ext.jussieu.fr>
> Sent: Sunday, November 05, 2006 1:28 AM
> Subject: Re: Observation on A053669
> 
> 
> > Yes,
> > and because a(n_odd)=2
> > keep only even n's.
> > Zak 
> 
> 



 
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