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

2, 4, 5, 12, 15, 15, 33, 53, 36, 41, 55, 51, 59, 91, 81, 60, 131, 167, 173, 312, 213, 394, 309, 222, 356, 868, 351, 704, 526, 1190, 1314, 847, 1435, 1148, 1755, 1499, 1797, 1455, 2311, 1863, 1838, 2120, 2859, 3219, 3463, 2833, 1723, 3009, 3497, 5886, 3746

Offset: 2

Author

Jon E. Schoenfield, Sep 03 2018

Keywords

• nonn
• base

Comments

For the corresponding values of k^n, see A318779.

Examples

			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.
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.
a(16)=81: 81^16 = 3433683820292512484657849089281 = 2b56d4af8f7932278c797ebd01_16.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..229 (terms 2..165 from Jon E. Schoenfield)

Crossrefs

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).

Programs

Python

from itertools import count
from sympy import integer_nthroot
from sympy.ntheory import digits
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

Formula

a(n) = A318779(n)^(1/n).