Vol. 8, No. 3, 2015

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Persistence: a digit problem

Stephanie Perez and Robert Styer

Vol. 8 (2015), No. 3, 439–446
Abstract

We examine the persistence of a number, defined as the number of iterations of the function which multiplies the digits of a number until one reaches a single digit number. We give numerical evidence supporting Sloane’s 1973 conjecture that there exists a maximum persistence for every base. In particular, we give evidence that the maximum persistence in each base 2 through 12 is 1, 3, 3, 6, 5, 8, 6, 7, 11, 13, 7, respectively.

Keywords
persistence, digit problem, multiplicative persistence, iterated digit functions
Mathematical Subject Classification 2010
Primary: 00A08, 97A20
Milestones
Received: 19 May 2013
Revised: 9 September 2013
Accepted: 23 December 2013
Published: 5 June 2015

Communicated by Kenneth S. Berenhaut
Authors
Stephanie Perez
Department of Mathematics and Statistics
Villanova University
800 Lancaster Avenue
Villanova, PA 19085-1699
United States
Robert Styer
Department of Mathematics and Statistics
Villanova University
800 Lancaster Avenue
Villanova, PA 19085-1699
United States