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On consecutive numbers of the same height in the Collatz problem

✍ Scribed by Guo-Gang Gao

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 404 KB
Volume: 112
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90240-t

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✦ Synopsis

Gao, G.-G., On consecutive numbers of the same height in the Collatz problem, Discrete Mathematics 112 (1993) 261-267.

The Collatz function C(n) is defined to take odd numbers n to 3n + 1 and even numbers n to n/2. This note presents computational results on consecutive numbers that have the same height and the same total stopping time by the Collatz function. A 35654-tuple of consecutive numbers was found. In consequence there exist infinitely many such 35654-tuples. A heuristic is given for estimating how long consecutive runs of the same height and the same total stopping time should be.

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