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A130083 Smallest number whose ninth power has at least n digits.

%I A130083 #14 Jun 20 2024 14:47:18
%S A130083 1,2,2,3,3,4,5,6,8,10,13,17,22,28,36,47,60,78,100,130,167,216,279,360,
%T A130083 465,600,775,1000,1292,1669,2155,2783,3594,4642,5995,7743,10000,12916,
%U A130083 16682,21545,27826,35939,46416,59949,77427,100000,129155,166811,215444
%N A130083 Smallest number whose ninth power has at least n digits.
%C A130083 Powers of ninth root of 10 rounded up.
%H A130083 Vincenzo Librandi, <a href="/A130083/b130083.txt">Table of n, a(n) for n = 1..1000</a>
%F A130083 a(n) = ceiling(10^((n-1)/9)).
%e A130083 2^9 = 512 has three digits, 3^9 = 19683 has five digits, hence a(4) = a(5) = 3.
%t A130083 Table[(Ceiling[10^((n - 1)/9)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 21 2013 *)
%o A130083 (Magma) [ Ceiling(Root(10^(n-1),9)): n in [1..49] ];
%o A130083 (Python)
%o A130083 from sympy import integer_nthroot
%o A130083 def A130083(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),9)) # _Chai Wah Wu_, Jun 20 2024
%Y A130083 Cf. A011278, A011557 (powers of 10), A017936 (smallest number whose square has n digits), A018005 (smallest number whose cube has n digits), A018074 (smallest number whose fourth power has n digits), A018143 (smallest number whose fifth power has n digits), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).
%K A130083 nonn,base,easy
%O A130083 1,2
%A A130083 _Klaus Brockhaus_, May 07 2007