login
Largest exclusionary n-th power (or 0 if no such number exists).
1

%I #9 Mar 14 2015 01:08:28

%S 408540845584,449103134312,51050010415041,0,606355001344,

%T 60170087060757,66045000696445844586496,0,3570467226624,743008370688,

%U 16777216,0,9012061295995008299689,0,1853020188851841,0,0,1162261467,1099511627776

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

%C 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.

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

%e 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.

%Y Cf. A112735, A112993, A113317.

%K base,nonn,fini

%O 2,1

%A _Lekraj Beedassy_, Nov 09 2005