Happy Numbers and Fixed Points
DOI:
https://doi.org/10.35819/remat2023v9i1id6190Keywords:
Happy Numbers, Fixed Points, Sequence of IntegersAbstract
This paper presents a brief study about the set of happy numbers, in any positional basis b>=2. We show examples of happy numbers and verify that every positive integer is happy in basis 4, Example 2.8. In particular, we characterize the fixed points of the happiness function, Theorem 3.2, which assigns to every positive integer the sum of the squares of its digits. In addition, techniques to determine the fixed points of the happiness function are showed, Theorem 3.5, Examples 3.7 and 3.8, in any positional basis.
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https://orcid.org/0000-0002-0893-7426
