[seqfan] Re: sparse odd entries

[M. F. Hasler]

On Thu, Apr 13, 2017 at 3:25 PM, David Newman <davidsnewman at gmail.com>
wrote:

> I'm looking for sequences which have few entries which are odd.
> Is there some easy way to search for such sequences?
>

I don't really have a good answer to that question(*), but the "sparse odd"
type sequences you mention include all characteristic functions of sets
with sufficiently low density
(i.e., a(n) = 1 if n is in Axxx, or 0 else, with Axxx sufficiently growing).
So, when a large integer is in the three lines of data (search for any
nunber greater than, say, 1000), then the characteristic function of that
sequence is very likely of the "sparse odd" type.

This makes me think of two (or more) missing keywords/Categories,
I think it would be useful if there was a way to select :
- strictly increasing sequences, which are those that represent sets
- sequences with only very small ranges, e.g.,:
-- all terms in {0,1}: these are characteristic functions, which would
merit a Category on their own;
-- sequences which are *bounded*: certainly also worth a Category on their
own.

(*) Some of the sequences with only very few odd terms might be found by
doing a search for many even terms (with the subseq: qualifier, or
separated by spaces instead of ","): if there are almost 3 lines (say, at
least one line) of even terms, there's not much place for many odd terms
in-between.

- Maximilian
<http://list.seqfan.eu/>