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

2,1

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.

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

Table of n, a(n) for n=2..20.

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

Example

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.

Crossrefs

Cf. A112735, A112993, A113317.

Sequence in context: A357687 A363799 A082411 * A375647 A218865 A289111

Adjacent sequences: A113949 A113950 A113951 * A113953 A113954 A113955

Keyword

base,nonn,fini

Author

Lekraj Beedassy, Nov 09 2005

Status

approved