A204047 Smallest number that is n-persistent but not (n+1)-persistent, i.e., k, 2k, ..., nk, but not (n+1)k, are pandigital in the sense of A171102; 0 if such a number does not exist.

1023456798, 1023456789, 1052674893, 1053274689, 13047685942, 36492195078, 153846076923, 251793406487, 0, 1189658042735, 5128207435967, 3846154076923, 125583660720493, 125583660493072, 180106284973592, 201062849735918

Offset: 1

Author

Hans Havermann, Jan 09 2012

Keywords

• nonn
• base

Comments

a(9) is 0 because any 9-persistent number is also 10-persistent. Indeed, if n is pandigital, 10*n is pandigital as well.

In the same way, a(10m-1)=0 for all m>0 since if kn is pandigital for all k=1,...,10m-1, then mn is pandigital and so is 10mn. - M. F. Hasler, Jan 10 2012

Examples

			k=36492195078 is the smallest number such that k, 2k, 3k, 4k, 5k, and 6k, each contain all ten digits, but 7k=255445365546 contains only five of the ten, so a(6)= 36492195078.
		

References

• Ross Honsberger, More Mathematical Morsels, Mathematical Association of America, 1991, pages 15-18.

Crossrefs

Cf. A051264, A051018, A051019, A051020, A204096, A204097.

Extensions

a(7)-a(16) from Giovanni Resta, Jan 10 2012