A133208 a(n) is the smallest number k such that k^n has the same digits as some other n-th power without leading zeros.

12, 12, 5, 4, 348, 731, 1001, 1001, 3747, 6526, 10001, 3967, 19365, 29088, 9436, 53331, 30484, 72091, 49255, 30342, 59579, 52604, 280501, 88379, 445885, 452341, 98107, 755179, 490404, 126493, 205417, 170613, 781944, 821573, 1808904, 209732, 1470036, 559096, 946969

Offset

1,1

Comments

The case where 10^n has the same digits as 1^n is excluded by no leading zeros constraint.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..105

Example

12^2 = 144 - the same digits as 21^2 = 441.
5^3 = 125 - the same digits as 8^3 = 512.
4^4 = 256 - the same digits as 5^4 = 625.
348^5 = 5103830227968 - the same digits as 381^5 = 8028323765901.

Prog

(Python)
from collections import Counter
def key(n):
    c = Counter(str(n))
    return tuple(c[i] for i in "0123456789")
def a(n):
    j, jn, jkey, repeated = 1, 1, key(1), []
    while not repeated:
        d, ub = dict(), 10**(sum(jkey))
        while jn <= ub:
            if jkey not in d: d[jkey] = j
            else: repeated.append(d[jkey])
            j += 1
            jn = j**n
            jkey = key(jn)
    return min(repeated)
print([a(n) for n in range(1, 25)]) # Michael S. Branicky, Dec 12 2021

Crossrefs

Sequence in context: A281251 A247511 A097824 * A118877 A112124 A268916

Adjacent sequences: A133205 A133206 A133207 * A133209 A133210 A133211

Keyword

base,nonn

Author

Tanya Khovanova, Oct 10 2007

Extensions

a(6)-a(34) from Donovan Johnson, Apr 22 2008

a(35)-a(39) from Chai Wah Wu, Jun 01 2020

a(1) from Chai Wah Wu, Jun 02 2020

Status

approved