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%I #16 Mar 13 2024 15:37:11
%S 4,64,625,248832,11390625,170859375,1406408618241,3299763591802133,
%T 3656158440062976,550329031716248441,766217865410400390625,
%U 15791096563156692195651,6193386212891813387462761,243008175525757569678159896851,3433683820292512484657849089281
%N Smallest n-th power that is pandigital in base n.
%C For the corresponding n-th roots a(n)^(1/n), see A318780.
%H Jon E. Schoenfield, <a href="/A318779/b318779.txt">Table of n, a(n) for n = 2..165</a>
%F a(n) = A318780(n)^n.
%e a(2)=4 because 1^2 = 1 = 1_2 (not pandigital in base 2, since it contains no 0 digit), but 2^2 = 4 = 100_2.
%e a(3)=64 because 1^3 = 1 = 1_3, 2^3 = 8 = 22_3, and 3^3 = 27 = 1000_3 are all nonpandigital in base 3, but 4^3 = 64 = 2101_3.
%e a(16) = 81^16 = 3433683820292512484657849089281 = 2b56d4af8f7932278c797ebd01_16.
%o (Python)
%o from itertools import count
%o from sympy import integer_nthroot
%o from sympy.ntheory import digits
%o def A318779(n): return next(k for k in (k**n for k in count(integer_nthroot((n**n-n)//(n-1)**2+n**(n-2)*(n-1)-1,n)[0])) if len(set(digits(k,n)[1:]))==n) # _Chai Wah Wu_, Mar 13 2024
%Y Cf. A049363 (smallest pandigital number in base n), A185122 (smallest pandigital prime in base n), A260182 (smallest square that is pandigital in base n), A260117 (smallest triangular number that is pandigital in base n), A318725 (smallest k such that k! is pandigital in base n), A318780 (smallest k such that k^n is pandigital in base n).
%K nonn,base
%O 2,1
%A _Jon E. Schoenfield_, Sep 03 2018