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arXiv · 1611.02983

Fixed Points of Augmented Generalized Happy Functions

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

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 $§_{[c,b]}$, for $b \geq 2$ and $0<c<3b-3$; and prove that, for each $b \geq 2$, there exist arbitrarily many consecutive values of $c$ for which $S_{[c,b]}$ has no fixed point.

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Breeanne Baker Swart, Kristen A. Beck, Susan Crook, Christina Eubanks-Turner, Helen G. Grundman, May Mei, Laurie Zack. 2016-11-09. Fixed Points of Augmented Generalized Happy Functions. https://arxiv.org/abs/1611.02983

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