[seqfan] Re: sparse odd entries

[Peter Munn]

On Thu, 13 April, 2017 8:25 pm, David Newman wrote:
> I'm looking for sequences which have few entries which are odd.
> A117958 which has a(n) congruent to 1 (mod 2) only for n=m squared,
> and m not divisible by 3 is an example of what I'm looking for. Is
> there some easy way to search for such sequences?

Hi David,

The only thing I can add to the answers of others is that searching for
comments seems to yield a high density of suitable sequences with
well-chosen search terms.  The numbers quoted below, though, are the total
number of search results:

"most terms are even" gives 2
"few odd terms" gives 3
"first odd term" gives 18
"only odd term" gives 19
"last odd term" gives 9
"smallest odd term" gives 3
"largest odd term" gives 4
"known odd terms" gives 1
"rare odd" gives 1

Sometimes the density of good results is much improved by specifying that
the search apply to the comments only, for example:

[comment:"first odd number"] gives 12
[comment:"last odd number"] gives 10

Combining a search for comments with a search on the sequence terms can
work even better.  The following seems to have many good examples amongst
its list:

[comment:"odd term" 2 4 8 -seq:3 -seq:5 -seq:7 -seq:9 -seq:11 -seq:13]
gives 43

Best Regards,

Peter