Kimberlike sequences

[Eric Angelini]

[Paul] :

> Perhaps a deeper look at the hidden structure beneath 
  Clark Kimberling's sequences will shed light on yours. 

... thank you, Paul, for this interesting post -- and no, I had
never heard before about Beatty sequences. I will plunge asap into
this matter and try to see if it can be of any help in answering
my questions.
Thanks again -- and especially for this:

> Here is how to determine the parameter r of the Beatty sequences
> from the distance factor d.
> The r is a root of quadratic equation 1 - d*x - x^2 = 0, or 
> r=(sqrt(d^2+4)-d)/2.

... Very interesting !
Best,
É.