A094091

[Joshua Zucker]

Hi seqfans,

I'm trying to extend Neil's sequence A094091

I get 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 with only 23 terms
by the greedy algorithm -- no 31 terms here!

But I'm not 100% certain that my code is working correctly.  The fact
that my first 16 terms match Neil's is reassuring, though.

The reason I'm suspicious:  Neil was curious in the comments about
what happens when S is set to 3 or 4.

I set S to 3 instead of 2, and still got only 23 terms!  (upper bound
with nongreedy algorithm is something like 900)
0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1
but since they were different terms, and had the obvious expected
number of leading zeros, I am still reasonably confident of my code.

Setting S to 4 and using that greedy algorithm I get 28 terms, (upper
bound with nongreedy algorithm being more than 100 thousand terms!)
0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0

If you can do something to help check these, that would be great!

Thanks,

--Joshua Zucker