A113952 Largest exclusionary n-th power (or 0 if no such number exists).

408540845584, 449103134312, 51050010415041, 0, 606355001344, 60170087060757, 66045000696445844586496, 0, 3570467226624, 743008370688, 16777216, 0, 9012061295995008299689, 0, 1853020188851841, 0, 0, 1162261467, 1099511627776

Offset: 2

Author

Lekraj Beedassy, Nov 09 2005

Keywords

• base
• nonn
• fini

Comments

An exclusionary n-th power m^n is one made up of digits not appearing in the root m which itself consists of distinct digits. For the corresponding root m, see A113951. In principle, no exclusionary n-th power exists for n=1(mod 4)=A016813.

Examples

			a(10)=3570467226624 because it shares no digit in common with its 10th root 18 and no number with distinct digits greater than 18 exhibits such property.
		

References

• H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9 Journal of Recreational Mathematics, Vol. 32 No.4 2003-4 Baywood NY.

Links

• Shyam Sunder Gupta, Elegance of Squares, Cubes, and Higher Powers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 2, 29-81.

Crossrefs

Cf. A112735, A112993, A113317.