[seqfan] Re: Destinies of sums of proper divisors.
David Wilson
dwilson at gambitcomm.com
Mon Jul 6 15:25:28 CEST 2009
I believe the proper terms are:
"trajectory of n" for the sequence
t(k) =
n if k = 0
f(t(k-1)) if k > 0
"attractor" for a set S with f(S) = S. (that is, the set of values in a
trajectory loop).
"fixpoint" for a single-element attractor (that is, {n} or n with f(n) = n).
"stopping point" for an element satisfying an artificial "stopping
condition", such as n = 1 for Collatz or f(n+1) <= n for the sequence in
question.
So "stopping point with condition f(n+1) <= n" would avoid having to
coin new terms.
franktaw at netscape.net wrote:
> Please don't call this the "destiny". Destiny implies where you wind
> up. "First decrease" would be fine, if nobody comes up with something
> better.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Maximilian Hasler <maximilian.hasler at gmail.com>
>
> I suggest a different notion of "destiny"
> (or someone may find a better name),
> namely, the first term in the trajectory under
> s(n)=sigma(n)-n
> which is not larger than its predecessor:
>
> ...
>
>
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