x->x*ceiling(x)

[John Conway]

On Thu, 29 Aug 2002, Richard Guy wrote:

> These are something like what I was calling
> `pseudo-GPs' and may be connected with PV numbers.
> I'm copying this message to him in the hope that
> he can put me right (or wrong!)  R.

   Dunno who "him" was, but can say I had a similar
feeling.  What Richard calls "pseudo-GPs" have also
been called "Pisot sequences", because P raised
the question whether they all satisfied recurrence
relations.  

    Astonishingly many of them do, but it's been
shown (does anyone know by whom?) that the one that
starts with  14,23  doesn't.

    The definition is that the number  c  that follows
a,b  is the nearest interger to  bb/a.  It doesn't
matter which nearest integer you take when there are
two, and wouldn't make much difference if "nearest
integer" were replaced by "integer part" or whatever.

    John Conway