Arnold's "strange infinite sequence of degrees"

[N. J. A. Sloane]

To Math-Fun, Seq-Fans:

There is an article by Arnold which has appeared in several places.
There are two versions in English:

MR2080045 Arnold, V. I. From Hilbert's superposition problem to dynamical systems [ MR1733564 (2001h:01031)].  Amer. Math. Monthly  111  (2004),  no. 7, 608--624. 01A65 (01A60 37-03 54H20)
 	
MR1733564 (2001h:01031) Arnold, V. I. From Hilbert's superposition problem to dynamical systems. The Arnoldfest (Toronto, ON, 1997), 1--18, Fields Inst. Commun., 24, Amer. Math. Soc., Providence, RI, 1999. (Reviewer: Stanis\l aw Janeczko) 01A65 (01A60 37-03 54H20)

Footnote 2 says:
"Starting from degree 9, one can kill one more coefficient. The
known possibilities to kill more coefficients occur along a rather 
strange infinite sequence of degrees."

He is refering to the problem of putting a polynomial equation 
f(X)=0 into canonical form. E.g. any 5th degree equation can be
reduced to  x^5 + aX + 1 = 0.

My question is, what is this "strange infinite sequence of degrees"?

Thanks

Neil Sloane