Possible Permutations With Mod

[Ferenc Adorjan]

Dear Seqfans,

After studying further the sequences of Leroy Quet (A125715, A125717,
A125718 & A125727), I am doubting now that they were permutations of
positive integers. Instead, these seqeunces seem consisting of an infinite
number of disjoint "chains" of infinite length (such that a(a(...a(n))) is
also a member of the sequence for any depth, while n is missing). This
statement is based on numerical explorations made on 25000 and also on 50000
elements of the sequences. More detailed info can be found in:
http://web.axelero.hu/fadorjan/l_quet.pdf
(the draft is substantially revised since my previous communication!)
I am curious, if anybody can propose some formal proof relating the nature
of this class of sequences...
Or, any other comments are welcome.
Regards

Ferenc
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