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%I A371706 #27 Apr 08 2024 18:46:11
%S A371706 1,4,4,2,3,3,4,3,2,1,1,1,1,1,1,1,1,1,1,4,1,3,3,3,3,3,3,3,2,4,1,2,2,2,
%T A371706 2,2,2,2,2,2,1,2,2,2,3,2,3,3,2,3,1,3,3,2,3,2,3,3,2,3,1,4,4,3,4,4,4,3,
%U A371706 2,4,1,2,3,5,3,4,4,4,2,3,1,3,3,4,3,4,4,3,2,2,1,4,4,6,4,2,3,3,2
%N A371706 a(n) is the least k > 0 such that n^k contains the digit 1.
%C A371706 First n such that a(n) = k: 1, 4, 5, 2, 74, 94, 305, 2975 for k = 1 to 8.
%C A371706 a(n) <= 8 for n <= 240000000.  Is a(n) ever greater than 8?
%C A371706 a(n) <= 8 for n <= 10^11. Moreover the only n <= 10^11 with a(n) = 8 are 2975 * 10^j. - _Robert Israel_, Apr 05 2024
%C A371706 a(n) <= 8 for n <= 10^13, and a(n) <= 17 for all n; see A275533. - _Michael S. Branicky_, Apr 08 2024
%H A371706 Robert Israel, <a href="/A371706/b371706.txt">Table of n, a(n) for n = 1..10000</a>
%F A371706 a(n) <= A098174(n).
%e A371706 a(3) = 4 because 3^1, 3^2 = 9 and 3^3 = 27 have no 1's, but 3^4 = 81 does have a 1.
%p A371706 g:= proc(n) local k;
%p A371706    for k from 1 do if member(1,convert(n^k,base,10)) then return k fi od;
%p A371706 end proc:
%p A371706 map(g, [$1..100]);
%t A371706 seq={};Do[k=1;While[!ContainsAny[IntegerDigits[n^k],{1}],k++];AppendTo[seq,k],{n,99}];seq (* _James C. McMahon_, Apr 05 2024 *)
%o A371706 (Python)
%o A371706 from itertools import count
%o A371706 def A371706(n):
%o A371706     m = n
%o A371706     for k in count(1):
%o A371706         if '1' in str(m):
%o A371706             return k
%o A371706         m *= n # _Chai Wah Wu_, Apr 04 2024
%Y A371706 Cf. A098174, A255430, A255357, A275533.
%K A371706 nonn,base
%O A371706 1,2
%A A371706 _Robert Israel_, Apr 03 2024

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