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On heights in the Collatz 3n + 1 problem

✍ Scribed by Lynn E. Garner


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
345 KB
Volume
55
Category
Article
ISSN
0012-365X

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✦ Synopsis


In the Collatz problem, certain runs of consecutive integers have the same height. This phenomenon is investigated using an algorithm for reconstructing the trajectory of a number from the parity vector of the number. It is found that pain of consecutive integers of the same height occur infinitely often and in infinitely many different patterns.


πŸ“œ SIMILAR VOLUMES


On consecutive numbers of the same heigh
✍ Guo-Gang Gao πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 404 KB

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 h

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We introduce a technical property (P) and use it to show that every M 3 -space with (P) is an M 1space whose every closed subset has a closure-preserving open neighborhood base. We show that every k-M 3 -space has property (P) and is, therefore, an M 1 -space.