cp's OEIS Frontend

A130084 Smallest number whose tenth power has at least n digits.

%I A130084 #18 Jun 20 2024 14:47:14
%S A130084 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 A130084 252,317,399,502,631,795,1000,1259,1585,1996,2512,3163,3982,5012,6310,
%U A130084 7944,10000,12590,15849,19953,25119,31623,39811,50119,63096,79433,100000
%N A130084 Smallest number whose tenth power has at least n digits.
%C A130084 Powers of tenth root of 10 rounded up.
%H A130084 Vincenzo Librandi, <a href="/A130084/b130084.txt">Table of n, a(n) for n = 1..1000</a>
%F A130084 a(n) = ceiling(10^((n-1)/10)).
%e A130084 3^10 = 59049 has five digits, 4^10 = 1048576 has seven digits, hence a(6) = a(7) = 4.
%t A130084 Table[(Ceiling[10^((n - 1)/10)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 20 2013 *)
%o A130084 (Magma) [Ceiling(Root(10^(n-1),10)): n in [1..51]];
%o A130084 (Python)
%o A130084 from sympy import integer_nthroot
%o A130084 def A130084(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),10)) # _Chai Wah Wu_, Jun 20 2024
%Y A130084 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 A130084 nonn,base,easy
%O A130084 1,2
%A A130084 _Klaus Brockhaus_, May 07 2007