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

%I #23 Jun 19 2020 21:28:07

%S 0,106,104,104,105,102,102,408,104,107,203,109,103,103,1056,3703,4604,

%T 207,606,11018,3069,20064

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

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

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

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

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

%o (Python)

%o def f(x):

%o for n in range(10**7):

%o if "0" in str(n):

%o if "0" not in str(n**x):

%o return n

%o for x in range(1, 75):

%o if f(x) is None:

%o print(0)

%o else:

%o print(f(x))

%Y Cf. A104315.

%K nonn,base,more,hard

%O 1,2

%A _Derek Orr_, Jan 02 2014

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