[seqfan] Re: Floretions, sufficient condition for conjecture

Creighton Kenneth Dement creighton.k.dement at mail.uni-oldenburg.de
Thu Jun 4 02:50:38 CEST 2009

> Dear Seqfans,
> I recently gave a list of five open conjectures.
> One of those conjectures is this one:
> X in Z^{infty} if and only if 4*tesseq(X) is a sequence of integers.

Update: Of the five conjectures listed here

conjectures 1 and 2 are now disproven. A counterexample is given at the
link above (for me, it was hard to believe this example after a couple
years of thinking otherwise).

Conjecture 4 has been shown to be a result of conjecture 3 (the one at the
top of this page). It is the content of corollaries 2.22/2.23 here:

So the big question left is whether conjecture 3 is valid. Note: I
previously added this sentence to the conjecture "Assume forall m: X^m !=
0" in an attempt to avoid the trivial counterexample X = 1/8('i + 'jj').
However, I forgot I mention in the introduction that the only fractional
parts allowed for all base coefficients of X must be in the set {+-0.25,
+-0.5, +- 0.75, 0}. Therefore, the counterexample does not apply.


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