A234966 Least number k with at least one zero such that k^n contains no zero, or 0 if no such number exists.

0, 106, 104, 104, 105, 102, 102, 408, 104, 107, 203, 109, 103, 103, 1056, 3703, 4604, 207, 606, 11018, 3069, 20064

Offset: 1

Author

Derek Orr, Jan 02 2014

Keywords

• nonn
• base
• more
• hard

Comments

a(n) > 5*10^8 or 0 for n = 23 and for 25 < n < 75.

It is known that a(24) = 12801714 and a(25) = 402.

a(n) > 5*10^9 or 0 for n = 23 and for 25 < n <= 200. - Chai Wah Wu, Apr 25 2019

Examples

			a(5) = 105 because 105 is the smallest number with a 0 where 105^5 does not have a 0 (105^5 = 12762815625).
		

Crossrefs

Cf. A104315.

Programs

Python

def f(x):
    for n in range(10**7):
        if "0" in str(n):
            if "0" not in str(n**x):
                return n
for x in range(1, 75):
    if f(x) is None:
        print(0)
    else:
        print(f(x))