Open Access
2018 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
Rocky Mountain J. Math. 48(1): 47-58 (2018). DOI: 10.1216/RMJ-2018-48-1-47


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 pro\-perties of the fixed points of $S_{[c,b]} $; count the number of fixed points of $S_{[c,b]} $ for $b \geq 2$ and $0\lt c\lt 3b-3$; 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. "Fixed points of augmented generalized happy functions." Rocky Mountain J. Math. 48 (1) 47 - 58, 2018.


Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 06866699
MathSciNet: MR3795732
Digital Object Identifier: 10.1216/RMJ-2018-48-1-47

Primary: 11A63

Keywords: Fixed points , happy numbers , integer functions , iteration

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.48 • No. 1 • 2018
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