[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.