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%I #24 Mar 14 2024 09:03:34
%S 2,4,5,12,15,15,33,53,36,41,55,51,59,91,81,60,131,167,173,312,213,394,
%T 309,222,356,868,351,704,526,1190,1314,847,1435,1148,1755,1499,1797,
%U 1455,2311,1863,1838,2120,2859,3219,3463,2833,1723,3009,3497,5886,3746
%N a(n) is the smallest positive integer k such that k^n is pandigital in base n.
%C For the corresponding values of k^n, see A318779.
%H Chai Wah Wu, <a href="/A318780/b318780.txt">Table of n, a(n) for n = 2..229</a> (terms 2..165 from Jon E. Schoenfield)
%F a(n) = A318779(n)^(1/n).
%e a(2)=2 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)=4 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: 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 A318780(n): return next(k 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,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), A318779 (smallest n-th power that is pandigital in base n).
%K nonn,base
%O 2,1
%A _Jon E. Schoenfield_, Sep 03 2018
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