Re: Collatz nature

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2022-01-05 09:36, Ruud H.G. van Tol wrote:
> On 2022-01-04 13:03, Ruud H.G. van Tol wrote:
> > On 2022-01-04 04:31, Ruud H.G. van Tol wrote:

> > > x -> (3x+1)/2
> > [...]
> > The inverse ("(x-1)/3") is always a sequence,
> > in which each element is one of:
> > - a dead end (0 == (x % 3)) (an "empty" sequence)
> > - in need of multiplication (2 == (x % 3)) (a singular)
> > - a sequence itself (1 == (x % 3))
>
> We started calling the sets like (3,1,2) "Cab numbers",
> because (a,b,c) = (1,2,3) in the order of "(3x+1)/2"
> spells cab.
>
> There are of course already Taxicab numbers (1729, Ramanujan),
> but it still feels fine as a casual name.
> (cab comes from capriole, the leap of a lamb)
>
> - - - - - - - -
>
> I'm now building a Perl module around it,
> using ideas from Math::Complex,
> to facilitate exploring.
>
> Because Perl has overload, and magic,
> it is a real nice environment to build such in.
>
> User code might then look like:
>
> my :i(1,2,3) $x= 9;
> say $x--, $x;  # 9, 7
>
> Etc.

Rather like:

my :cab(3,1,2) $x= 9;

:)

-- Ruud