Ruud H.G. van Tol on Wed, 05 Jan 2022 10:13:24 +0100

 Re: Collatz nature

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On 2022-01-05 09:36, Ruud H.G. van Tol wrote:
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```On 2022-01-04 13:03, Ruud H.G. van Tol wrote:
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```On 2022-01-04 04:31, Ruud H.G. van Tol wrote:
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```x -> (3x+1)/2
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```[...]
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))
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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.
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Rather like:

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

:)

-- Ruud

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