More on Leroy Quet's permutation transform

[Leroy Quet]

David Wasserman wrote:
>To Leroy Quet: Do you think it's appropriate for me to refer to it as the 
>"Quet transform"?  Since no one has posted a reference, I'm assuming it's 
>original.  However, maybe you have invented (or will invent) some other 
>transform that you'd rather give your name to.
>
>v/r,
>David
>----------------------------------

Sure, why not.
I have thought up other transforms, but we can call this one Quet's 
transform involving permutations, or something.
:)




I have a conjecture for seq.fan that I am having trouble solving myself.

If your start sequence is:

1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6,...

([1,m] repeated),

then does the "Quet transform" yield

1, 1, 1, 2, 1, 2, 3, 1, 3, 4, 1, 4, 5, 1, 5,

([m,1,m] repeated)?

(So we have a sequence where the 1's occurring every 2 terms being 
transformed (maybe) into a sequence where the 1's occur every 3 terms.)

thanks,
Leroy Quet