[seqfan] Fwd: Iterates of n - A002828(n) ?

[Antti Karttunen]

Just wondering:

If we iterate the function a(n) = n - A002828(n) (
https://oeis.org/A002828) from any starting value k, will the
trajectory visit every square-1
(A005563) < k before it reaches zero?
Which would imply that there would be only one infinite sequence a_n such
that a(n-1) = a(n) - the least number of squares that add up to a(n).

Then, would there be any regularity in the derived sequence counting the
number of iterations needed to hop from A005563(n+1) to A005563(n) ?



Cheers,

Antti