A318779 Smallest n-th power that is pandigital in base n.

4, 64, 625, 248832, 11390625, 170859375, 1406408618241, 3299763591802133, 3656158440062976, 550329031716248441, 766217865410400390625, 15791096563156692195651, 6193386212891813387462761, 243008175525757569678159896851, 3433683820292512484657849089281

Offset

2,1

Comments

For the corresponding n-th roots a(n)^(1/n), see A318780.

Links

Jon E. Schoenfield, Table of n, a(n) for n = 2..165

Formula

a(n) = A318780(n)^n.

Example

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

Prog

(Python)
from itertools import count
from sympy import integer_nthroot
from sympy.ntheory import digits
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

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), A318780 (smallest k such that k^n is pandigital in base n).

Sequence in context: A224446 A128782 A353453 * A264567 A264575 A053957

Adjacent sequences: A318776 A318777 A318778 * A318780 A318781 A318782

Keyword

nonn,base

Author

Jon E. Schoenfield, Sep 03 2018

Status

approved