An -persistent number is a positive integer which contains the digits 0, 1, ..., 9 (i.e., is a pandigital number), and for which , ..., also share this property. No -persistent numbers exist. However, the number is 2-persistent, since but , and the number is 18-persistent. There exists at least one -persistent number for each positive integer .
Persistent Number
See also
Additive Persistence, Multiplicative Persistence, Pandigital NumberExplore with Wolfram|Alpha
References
Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 15-18, 1991.Sloane, N. J. A. Sequences A051018, A051019, A051020, and A051264 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Persistent NumberCite this as:
Weisstein, Eric W. "Persistent Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PersistentNumber.html