[seqfan] Duplicated "A*n+B" sequences
Robert Munafo
mrob27 at gmail.com
Mon Nov 30 11:32:49 CET 2009
These all fit into the same pattern, repeating the terms of a linear
sequence "A*n+B" (where A and B are integer constants, like 2n+1 which
is the odd numbers, see A109613)
All of these have an equally simple recurrence relation, for example
the "repeated 3n" sequence (0, 0, 3, 3, 6, 6, 9, 9, ...) is given by
A[0] = 0; A[n+1] = - A[n] + 3 n. Of course, a non-recurrence, direct
formula definition is at least as useful if not more; using the same
example we have A[n] = 3*floor(n/2).
The recurrence relation form is more universal because it also
provides for "staggering" or "three steps forward, two steps back"
type sequences. An example is 1,4,2,5,3,6,4,7,5,8,... which is defined
as A084964 and A097065, and given by A[0] = 1; A[n+1] = - A[n] + n.
All but the very lowest values of A and B have never been in EIS or
DBIS/OEIS until just this month. For example, the repeated even
numbers are A052928, but the "repeated 3n" sequence was only just
added to OEIS a couple weeks ago. It is A168237, and was added by
Vincenzo Librandi, who is also the author the doubled 4*n sequence
A168273, the doubled 5*n+1 sequence 168209, and the 9*n+B sequences
Paolo noticed. He also submitted many of the "staggering" type
sequences, for example 168230, 168232 and 168465.
I don't think any of these sequences is too useful, but I also feel
that way about a lot of other things that are in OEIS. I'm a bit
old-fashioned and I still think existing publication should be a
prerequisite (see Handbook of Integer Sequences, section 1.5, rule 4)
and that is why I create a web page for each sequence before
submitting it. But I recognize the fact that I am outnumbered and a
bit of an old relic in this regard.
- Robert Munafo
Alois Heinz wrote:
> Paolo Lava schrieb:
> > Hello Seqfans,
> >
> > Is it possible to create an "authomatic deletion procedure" in order to
> > avoid the duplication of the same sequence?
> >
> > e.g. A168414 & A168415
> I do not see any reason for any of the sequences to be listed in the OEIS.
> And the author gives us no reason and no explanation, information or
> inspiration.
>
> The sequence seems arbitrary and it is very simple, the given
> recursive formula is too complicated.
>
> "a(n)=9*n-a(n-1)-6 (with a(1)=6)" is the same as
>
> "a(n)=9*floor((n+1)/2)-3" which is easier to understand and to evaluate.
>
> I can not imagine who would do a search on
> 6, 6, 15, 15, 24, 24, 33, 33, 42, 42, 51, 51, 60, 60, ...
>
> At least the keywords should be a combination of dumb,less,easy
>
> There are more new sequences like these, e.g.:
> A168411|A168413|A168416|A168418|A168419|A168420
--
Robert Munafo -- mrob.com
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