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."
