Collatz conjecture

(notes by Roberto Bigoni)

Collatz sequence


A number c0 ≥ 1 generates a Collatz's sequence C if it is the first element of a sequence of natural numbers ci such that


If C contains the number 1, this number can be considered the last of the sequence, because from this number forward the sequence oscillates in the cycle 1-4-2-1.

We may conjecture that from whatever c0 a Collatz sequence starts, it reaches always 1.

Even though this conjecture has been tested for many numbers by calculation programs like the in the above form, it is not generally demonstrated for every natural number.

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Many mathematicians were involved in the search of a demonstration. See:

last reviewed: October 2018