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

2,1

Comments

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

Links

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

Formula

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

Example

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.

Prog

(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

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).

Sequence in context: A351753 A268530 A090847 * A056984 A117556 A091071

Adjacent sequences: A318777 A318778 A318779 * A318781 A318782 A318783

Keyword

nonn,base

Author

Jon E. Schoenfield, Sep 03 2018

Status

approved