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.

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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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 Number

Cite this as:

Weisstein, Eric W. "Persistent Number." From MathWorld--A Wolfram Web Resource.

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