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	Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages
	Swart, Breeanne Baker; Crook, Susan; Grundman, Helen G.; Hall-Seelig, Laura; Mei, May; Zack, Laurie
通讯作者	Swart, BB
来源期刊	JOURNAL OF INTEGER SEQUENCES
ISSN	1530-7638
出版年	2019
卷号	22 期号:5
英文摘要	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 >= 2 and k is an element of Z(+), a k-desert base b is a set of k consecutive non-negative integers c for each of which S([)(c,)(b] )has no fixed points. In this paper, we examine a complementary notion, a k-oasis base b, which we define to be a set of k consecutive non-negative integers c for each of which S-[(c,)b] has a fixed point. In particular, after proving some basic properties of oases base b, we compute bounds on the lengths of oases base b and compute the minimal examples of maximal length oases base b for small values of b.
英文关键词	happy number fixed point iteration
类型	Article
语种	英语
收录类别	ESCI
WOS记录号	WOS:000483312900005
WOS类目	Mathematics
WOS研究方向	Mathematics
资源类型	期刊论文
条目标识符	http://119.78.100.177/qdio/handle/2XILL650/333771
作者单位	[Swart, Breeanne Baker] The Citadel, Dept Math Sci, Charleston, SC 29409 USA; [Crook, Susan] Loras Coll, Div Math Engn & Comp Sci, 1450 Alta Vista St, Dubuque, IA 52001 USA; [Grundman, Helen G.] Bryn Mawr Coll, Dept Math, 101 N Merion Ave, Bryn Mawr, PA 19010 USA; [Hall-Seelig, Laura] Merrimack Coll, Dept Math, 315 Turnpike St, N Andover, MA 01845 USA; [Mei, May] Denison Univ, Dept Math & Comp Sci, 100 West Coll St, Granville, OH 43023 USA; [Zack, Laurie] High Point Univ, Dept Math Sci, One Univ Pkwy, High Point, NC 27268 USA
推荐引用方式 GB/T 7714	Swart, Breeanne Baker,Crook, Susan,Grundman, Helen G.,et al. Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages[J],2019,22(5).
APA	Swart, Breeanne Baker,Crook, Susan,Grundman, Helen G.,Hall-Seelig, Laura,Mei, May,&Zack, Laurie.(2019).Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages.JOURNAL OF INTEGER SEQUENCES,22(5).
MLA	Swart, Breeanne Baker,et al."Fixed Points of Augmented Generalized Happy Functions II: Oases and Mirages".JOURNAL OF INTEGER SEQUENCES 22.5(2019).