A130084 - OEIS

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

%S 1,2,2,2,3,4,4,6,7,8,10,13,16,20,26,32,40,51,64,80,100,126,159,200,

%T 252,317,399,502,631,795,1000,1259,1585,1996,2512,3163,3982,5012,6310,

%U 7944,10000,12590,15849,19953,25119,31623,39811,50119,63096,79433,100000

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

%C Powers of tenth root of 10 rounded up.

%H Vincenzo Librandi, <a href="/A130084/b130084.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 3^10 = 59049 has five digits, 4^10 = 1048576 has seven digits, hence a(6) = a(7) = 4.

%t Table[(Ceiling[10^((n - 1)/10)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 20 2013 *)

%o (Magma) [Ceiling(Root(10^(n-1),10)): n in [1..51]];

%o (Python)

%o from sympy import integer_nthroot

%o def A130084(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),10)) # _Chai Wah Wu_, Jun 20 2024

%Y Cf. A011279, 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 A130083 (smallest number whose sixth ... ninth power has n digits).

%K nonn,base,easy

%O 1,2

%A _Klaus Brockhaus_, May 07 2007