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
On heights in the Collatz 3n + 1 problem
β Scribed by Lynn E. Garner
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 345 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ 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.
π SIMILAR VOLUMES
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.