A130083 - OEIS

%I #14 Jun 20 2024 14:47:18

%S 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 465,600,775,1000,1292,1669,2155,2783,3594,4642,5995,7743,10000,12916,

%U 16682,21545,27826,35939,46416,59949,77427,100000,129155,166811,215444

%N Smallest number whose ninth power has at least n digits.

%C Powers of ninth root of 10 rounded up.

%H Vincenzo Librandi, <a href="/A130083/b130083.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling(10^((n-1)/9)).

%e 2^9 = 512 has three digits, 3^9 = 19683 has five digits, hence a(4) = a(5) = 3.

%t Table[(Ceiling[10^((n - 1)/9)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 21 2013 *)

%o (Magma) [ Ceiling(Root(10^(n-1),9)): n in [1..49] ];

%o (Python)

%o from sympy import integer_nthroot

%o def A130083(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),9)) # _Chai Wah Wu_, Jun 20 2024

%Y 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 nonn,base,easy

%O 1,2

%A _Klaus Brockhaus_, May 07 2007