Category Archives: Uncategorized

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 ofContinue reading “A perfect binary Collatz tree”

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 countingContinue reading “Collatz Proof”