[seqfan] Re: A133058

M. F. Hasler oeis at hasler.fr
Sun Feb 15 16:58:43 CET 2015

On Sun, Feb 15, 2015 at 10:30 AM, Allan Wechsler <acwacw at gmail.com> wrote:
> A comment by the author (Zizka) seems to recognize the possibility of these
> period-4 regimes. This leads me to think that one might devise a
> meta-sequence telling how soon the regime is entered depending on starting
> values.

Maybe, but note that A255140 enters a different loop, of form
(1,x,2x,x) and not (1,x,2x,2).
So actually we would have (at least) these 3 variants (**)
(with ...+n  vs. +n+1 and offset/indexing a[n-1] vs a[n])
and for each of these a meta sequence, function of the respective a[1].

(**) The a(n+1) = a(n)*2+1 resp. a(n)*3 variants do not have this
looping property, but each has its own self-similarity property, which
is for the latter also explained by the simple recurrence formula I
added for A253092 = log3 A133579.

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