21st Century Paradox
A perfect binary Collatz tree
To compute the OPI values in the tree…Let q = the quotient of the lower OPI and r = its residue mod 3: These rules will generate the identical OPI not ≡ 0 mod 3 found in the graph generated by the original Collatz function and will map onto the odd positive integer results of…
(q,r)(p,x) Collatz
A Word document… Supporting Excel spreadsheet referenced in the document above…
Collatz Decoded 17-12-25
A presentation in Word… An analysis of the Collatz function in Excel…
Decoding Collatz
Have a look at the spreadsheet…it should be self explanatory. If not, then send a question.
Collatz Proof
Consider the positive integers in base 2, in binary notation. Define prefix: the digits left of the first pair (from the right) of identical digits along with the left digit of that pair. Define tail: the digits to the right of the prefix. Define the Collatz function: Consider the positive integers in binary in counting…
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21st Century Paradox 