[seqfan] Re: Sequence with a strange for OEIS conjecture

[D. S. McNeil]

> A year ago, I introduced into OEIS sequence A174531, defined by a recursion, with a strange for OEIS conjecture:  all terms of this sequence are integers.  I wonder
> 1) whether exist other sequences in OEIS with such a strange for OEIS conjecture?

One reason it's a little unusual is because in general sequences that
aren't known to be integral are disfavoured.  (Yes, there are a fair
number of exceptions, and we can always rescue them by the usual "or
some-number-if-not-integral" or "integral terms generated by.."
tricks, but still.)

> 2) Can anyone  suggest a program for the calculation ? (the existing 42 calculated terms I found by handy).

I'm not sure about the last few of your terms: I find

[1, 1, 3, 4, 2, 4, 5, 25, 32, 3, 19, 32, 7, 77, 294, 384, 4, 52, 240,
384, 9, 174, 1323, 4614, 6144, 5, 110, 967, 3934, 6144, 11, 330, 4169,
27258, 90992, 122880, 6, 200, 2842, 21040, 79832, 122880]

but you have

[1, 1, 3, 4, 2, 4, 5, 25, 32, 3, 19, 32, 7, 77, 294, 384, 4, 52, 240,
384, 9, 174, 1323, 4614, 6144, 5, 110, 967, 3934, 6144, 11, 330, 4169,
27258, 90992, 122880, 6, 200, 3342, 22540, 81332, 123380]

I'm not totally sure of mine, or I'd make the correction.  Anyone
confirm?  BTW, adding a brief explanation of the motivation for the
polynomials might be a good idea..  Right now it seems like they fell
out of the sky.


Doug