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Persistent Number

An n-persistent number is a positive integer k which contains the digits 0, 1, ..., 9 (i.e., is a pandigital number), and for which 2k, ..., nk also share this property. No infty-persistent numbers exist. However, the number k=1234567890 is 2-persistent, since 2k=2469135780 but 3k=3703703670, and the number k=526315789473684210 is 18-persistent. There exists at least one k-persistent number for each positive integer k.

nOEISn-persistent
1A0512641023456798, 1023456897, 1023456978, 1023456987, ...
2A0510181023456789, 1023456879, 1023457689, 1023457869, ...
3A0510191052674893, 1052687493, 1052746893, 1052748693, ...
4A0510201053274689, 1089467253, 1253094867, 1267085493, ...

See also

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

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