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A318780 a(n) is the smallest positive integer k such that k^n is pandigital in base n.

%I A318780 #24 Mar 14 2024 09:03:34
%S A318780 2,4,5,12,15,15,33,53,36,41,55,51,59,91,81,60,131,167,173,312,213,394,
%T A318780 309,222,356,868,351,704,526,1190,1314,847,1435,1148,1755,1499,1797,
%U A318780 1455,2311,1863,1838,2120,2859,3219,3463,2833,1723,3009,3497,5886,3746
%N A318780 a(n) is the smallest positive integer k such that k^n is pandigital in base n.
%C A318780 For the corresponding values of k^n, see A318779.
%H A318780 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 A318780 a(n) = A318779(n)^(1/n).
%e A318780 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 A318780 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 A318780 a(16)=81: 81^16 = 3433683820292512484657849089281 = 2b56d4af8f7932278c797ebd01_16.
%o A318780 (Python)
%o A318780 from itertools import count
%o A318780 from sympy import integer_nthroot
%o A318780 from sympy.ntheory import digits
%o A318780 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 A318780 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 A318780 nonn,base
%O A318780 2,1
%A A318780 _Jon E. Schoenfield_, Sep 03 2018