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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Divisibility by $ 2$ of Stirling-like numbers


Author: Donald M. Davis
Journal: Proc. Amer. Math. Soc. 110 (1990), 597-600
MSC: Primary 11B73
DOI: https://doi.org/10.1090/S0002-9939-1990-1036984-4
MathSciNet review: 1036984
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Abstract: We give a characterization of functions of the form $ f(n) = \nu (n - E)$, where $ \nu ( - )$ denotes the exponent of 2, and $ E$ is a $ 2$-adic integer. We show that it applies to the restriction to even or odd integers of the function $ f(n) = \nu (a{5^n} + b{3^n} + c)$, with mild restrictions on $ a,b$, and $ c$. This function is closely related to divisibility of certain Stirling numbers of the second kind.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1036984-4
Keywords: Stirling numbers, divisibility by 2, $ 2$-adic integers
Article copyright: © Copyright 1990 American Mathematical Society