cp's OEIS Frontend

A130082 Smallest number whose eighth power has at least n digits.

%I A130082 #15 Jun 20 2024 14:47:22
%S A130082 1,2,2,3,4,5,6,8,10,14,18,24,32,43,57,75,100,134,178,238,317,422,563,
%T A130082 750,1000,1334,1779,2372,3163,4217,5624,7499,10000,13336,17783,23714,
%U A130082 31623,42170,56235,74990,100000,133353,177828,237138,316228,421697
%N A130082 Smallest number whose eighth power has at least n digits.
%C A130082 Powers of eighth root of 10 rounded up.
%H A130082 Vincenzo Librandi, <a href="/A130082/b130082.txt">Table of n, a(n) for n = 1..1000</a>
%F A130082 a(n) = ceiling(10^((n-1)/8)).
%e A130082 9^8 = 43046721 has eight digits, 10^8 = 100000000 has nine digits, hence a(9) = 10.
%t A130082 Table[(Ceiling[10^((n - 1)/8)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 20 2013 *)
%o A130082 (Magma) [ Ceiling(Root(10^(n-1),8)): n in [1..46] ];
%o A130082 (Python)
%o A130082 from sympy import integer_nthroot
%o A130082 def A130082(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),8)) # _Chai Wah Wu_, Jun 20 2024
%Y A130082 Cf. A011277, 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 A130082 nonn,base,easy
%O A130082 1,2
%A A130082 _Klaus Brockhaus_, May 07 2007