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Persistent Number

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 .

 OEIS -persistent 1 A051264 1023456798, 1023456897, 1023456978, 1023456987, ... 2 A051018 1023456789, 1023456879, 1023457689, 1023457869, ... 3 A051019 1052674893, 1052687493, 1052746893, 1052748693, ... 4 A051020 1053274689, 1089467253, 1253094867, 1267085493, ...

Additive Persistence, Multiplicative Persistence, Pandigital Number

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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."

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Persistent Number

Cite this as:

Weisstein, Eric W. "Persistent Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PersistentNumber.html