|
|||||
 |
|
|
|
|
|
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 |
|
|
