A371706 - OEIS

%I #27 Apr 08 2024 18:46:11

%S 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 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 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 a(n) is the least k > 0 such that n^k contains the digit 1.

%C First n such that a(n) = k: 1, 4, 5, 2, 74, 94, 305, 2975 for k = 1 to 8.

%C a(n) <= 8 for n <= 240000000.  Is a(n) ever greater than 8?

%C 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 a(n) <= 8 for n <= 10^13, and a(n) <= 17 for all n; see A275533. - _Michael S. Branicky_, Apr 08 2024

%H Robert Israel, <a href="/A371706/b371706.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) <= A098174(n).

%e 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 g:= proc(n) local k;

%p    for k from 1 do if member(1,convert(n^k,base,10)) then return k fi od;

%p end proc:

%p map(g, [$1..100]);

%t seq={};Do[k=1;While[!ContainsAny[IntegerDigits[n^k],{1}],k++];AppendTo[seq,k],{n,99}];seq (* _James C. McMahon_, Apr 05 2024 *)

%o (Python)

%o from itertools import count

%o def A371706(n):

%o     m = n

%o     for k in count(1):

%o         if '1' in str(m):

%o             return k

%o         m *= n # _Chai Wah Wu_, Apr 04 2024

%Y Cf. A098174, A255430, A255357, A275533.

%K nonn,base

%O 1,2

%A _Robert Israel_, Apr 03 2024