A061724 Smallest number which has more different digits than its n-th power, or -1 if no such number exists.

109, 1920, 26730, 4385270, 13486709, 13652048, 134267085, 285963417, 341872690, 1032479568, 1026349857, 1027563984, 1029637584, 1239574806, 2059716348, 1654923078, 58157032649, 8152497360, 17345693802, 127601348591

Offset

2,1

Comments

a(22), a(23), a(24) > 2*10^11, if they exist. - Giovanni Resta, Aug 06 2019

Links

Table of n, a(n) for n=2..21.

Example

1920 is the smallest number which has more different digits than its cube (4 digits vs. 3 digits in 7077888000 = 1920^3), hence a(3) = 1920

Prog

(Python)
from itertools import count
def a(n): return next(k for k in count(1) if len(set(str(k))) > len(set(str(k**n))))
print([a(n) for n in range(2, 6)]) # Michael S. Branicky, May 25 2023

Crossrefs

Cf. A061277, A061374.

Sequence in context: A262854 A232118 A201849 * A145852 A232198 A232416

Adjacent sequences: A061721 A061722 A061723 * A061725 A061726 A061727

Keyword

nonn,base,hard,more

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Extensions

a(6) and a(7) from Stefan Steinerberger, Sep 07 2007

a(8)-a(17) from Sean A. Irvine, Dec 02 2010

a(18)-a(21) from Giovanni Resta, Aug 06 2019

Status

approved