Ruud H.G. van Tol on Tue, 04 Jan 2022 13:04:09 +0100

 Re: Collatz nature

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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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Corrected table:

p3:_9[_7]11|17|13[_5]_1|
p2:__|14|22|34|26|10|_2|
_____|28|__|__|52|20[_4]
_____|__|__|__|__|40|_8|
_____|__|__|__|__|__|16|

Corrections:
- marked 'next lower' with [].

- - - - - -

The sieve-formula for `9` is [2,9,1,7]
(i * 2^2 * x + 9) -> i * 3^1 * x + 7)
so p2=2 and p3=1. (9 is 4x+1)

The sieve-formula for `7` is [7,7,4,5]
(i * 2^7 * x + 7) -> i * 3^4 * x + 5)
so p2=7 and p3=4.

The sieve-formula for `5` is [2,5,1,4]
(i * 2^2 * x + 5) -> i * 3^1 * x + 4)
so p2=2 and p3=1. (5 is 4x+1)

The sieve-formula for `4` is [2,1,1,1]
(i * 2^2 * x + 1) -> i * 3^1 * x + 1)
so p2=2 and p3=1. (1 is 4x+1)

- - - - - -
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))

-- Ruud

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