Výsledky vyhledávání - "Crook, Susan"

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Autor: Swart, Breeanne Baker, Crook, Susan, Grundman, Helen G., Hall-Seelig, Laura

This paper extends the concept of a $B$-happy number, for $B \geq 2$, from the rational integers, $\mathbb{Z}$, to the Gaussian integers, $\mathbb{Z}[i]$. We investigate the fixed points and cycles of the Gaussian $B$-happy functions, determining the

Externí odkaz: http://arxiv.org/abs/2101.00560

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Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages

Autor: Swart, Breeanne Baker, Crook, Susan, Grundman, Helen G., Hall-Seelig, Laura, Mei, May, Zack, Laurie

An augmented generalized happy function $S_{[c,b]}$ maps a positive integer to the sum of the squares of its base $b$ digits plus $c$. For $b\geq 2$ and $k \in \mathbb{Z}^+$, a $k$-desert base $b$ is a set of $k$ consecutive non-negative integers $c$

Externí odkaz: http://arxiv.org/abs/1908.02194

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Fixed Points of Augmented Generalized Happy Functions

Autor: Swart, Breeanne Baker, Beck, Kristen A., Crook, Susan, Eubanks-Turner, Christina, Grundman, Helen G., Mei, May, Zack, Laurie

An augmented generalized happy function $S_{[c,b]}$ maps a positive integer to the sum of the squares of its base $b$ digits plus $c$. In this paper, we study various properties of the fixed points of $S_{[c,b]}$; count the number of fixed points of

Externí odkaz: http://arxiv.org/abs/1611.02983

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Augmented generalized happy functions

Autor: Swart, Breeanne Baker, Beck, Kristen A., Crook, Susan, Eubanks-Turner, Christina, Grundman, Helen G., Mei, May, Zack, Laurie

An augmented happy function, $S_{[c,b]}$ maps a positive integer to the sum of the squares of its base-$b$ digits and a non-negative integer $c$. A positive integer $u$ is in a cycle of $S_{[c,b]}$ if, for some positive integer $k$, $S_{[c,b]}^k(u) =

Externí odkaz: http://arxiv.org/abs/1410.0297

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