Queneau-Daniel permutation and type-2 ONB

[Joerg Arndt]

As communicated by Jean-Guillaume Dumas, the sequences

A054639 Queneau numbers: numbers n such that the Queneau-Daniel
permutation {1, 2, 3, ..., n} -> {n, 1, n-1, 2, n-2, 3, ...} is of
order n.

and

A135582 Values of n such that a type-2 optimal normal basis over GF(2)
exists.

are the same, see http://hal.archives-ouvertes.fr/hal-00188240/en
(if you understand French, I sadly do not).

Should we keep to separate seqs anyway?

I suggest to clarify the description of A135582 to
Values of n such that a type-2 optimal normal basis over GF(2^n) exists.
[Note the "GF(2^n)"]

cheers,  jj





Dear Joerg,  You used the phrase "a type-2 optimal normal basis over GF(2^n)".

Probably I do not understand your terminology.  But this looks
wrong to me.  Normally one speaks of a basis FOR a big field K
OVER a subfield k.

Did you mean to say:

"a type-2 optimal normal basis for GF(2^n) over GF(2)" ?

Neil




PS  Joerg asks if A054639 and A135582 should be merged.

Not until we have a proof that they are the same!

The present versions ask if they are the same,
and that is the correct way to handle this!

Neil