Scratch Notes on the Collatz Conjecture
Tables⌗
Least Significant Digit Multiplication Results⌗
There must be, on average, a 1:1 correspondance between additions and divisions
3 * ...0 + 1 = ...1 | d = 1
3 * ...1 + 1 = ...4 | d = 3
3 * ...2 + 1 = ...7 | d = 5
3 * ...3 + 1 = ....0 | d = 3
3 * ...4 + 1 = ....3 | d = 1
3 * ...5 + 1 = ....6 | d = 1
3 * ...6 + 1 = ....9 | d = 3
3 * ...7 + 1 = ....2 | d = 5
3 * ...8 + 1 = ....5 | d = 3
3 * ...9 + 1 = ....8 | d = 1
....0 / 2 = ...0 U ...5
....2 / 2 = ...1 U ...6
....4 / 2 = ...2 U ...7
....6 / 2 = ...3 U ...8
....8 / 2 = ...4 U ...9
Divisibility Representation⌗
Each digit is represented by a pair (t, r)
, where t
is the number of times that a digit can be divided by two, and r
is what that digit will become when divided with t = 0
.
When a pair with t = 0
is