[seqfan] Re: [SeqFan] Re: sparse odd entries

M. F. Hasler oeis at hasler.fr
Sat Apr 15 17:52:21 CEST 2017

On Sat, Apr 15, 2017 at 9:51 AM, Frank Adams-Watters via SeqFan
<seqfan at list.seqfan.eu> wrote:
> Is A000984 the sort of thing you are looking for?

I think this (only one, or even finitely many terms) is a degenerate
(and maybe somewhat less interesting) case of "sparse".

> Also A000108, not quite as sparse.

as are all others with a(n) mod 2 = A036987, characteristic function
of A000225 (2^n-1):
A001700, A005573, A007854, A026641, A049027, A064063, A064088,
A064090, A064092, A064325, A064327, A064329, A064331, A064613,
A076026, A105523, A123273, A126694, A126930, A126931, A126982,
A126983, A126987, A127016, A127053, A127358, A127360, A127361,
A127363, ...

- Maximilian

PS (mainly to OEIS wizards): I just got an idea to improve search
performance for sequences with most/any terms < 2 in absolute value:
(It's well known that for these, the otherwise amazingly efficient
search algorithm is that catastrophic that even an optimally designed
search with more than 100 terms provided easily takes 30-60 seconds
and almost constitutes a DoS attack.)
For those, a special index could be created, which stores the first
differences of indices of nonzero terms. E.g., a sequence (or search
for) "1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1" would be coded as "1,3,7,15" w.r.t. that
special index.
(Using the first differences has the advantage of independence of the
offset / position at which that (sub)sequence occurs.)

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