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

Marc LeBrun mlb at well.com
Tue Sep 27 20:44:39 CEST 2011

>="Vladimir Shevelev" <shevelev at bgu.ac.il>
> I wonder
1) whether exist other sequences in OEIS with such a strange
> for OEIS conjecture [ all terms of this sequence are integers]?

>="D. S. McNeil" <dsm054 at gmail.com>
> 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.)

>=" Franklin T. Adams-Watters" <franktaw at netscape.net>
> I don't know that that's true. I think it's just that such sequences are
> relatively rare; usually, you can either find a non-integer value or prove
> that all terms are integers fairly easily.

Yes, usually.  

One remarkable exception to this rule-of-thumb are the "Somos Sequences"

BTW along with the "rescues" mentioned above, for rational sequences there's
also often the possibility of submitting both the numerator and denominator

Of course that doesn't help if there are values such as "infinity" or "?"
(perhaps such as a(4) in A001676?).  Or worse, "coffee cup" as in A193616!

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