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, ...

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."