cp's OEIS Frontend

A130080 Smallest number whose sixth power has n digits.

%I A130080 #14 Jun 19 2024 15:40:04
%S A130080 1,2,3,4,5,7,10,15,22,32,47,69,100,147,216,317,465,682,1000,1468,2155,
%T A130080 3163,4642,6813,10000,14678,21545,31623,46416,68130,100000,146780,
%U A130080 215444,316228,464159,681293,1000000,1467800,2154435,3162278,4641589
%N A130080 Smallest number whose sixth power has n digits.
%C A130080 Powers of sixth root of 10 rounded up.
%H A130080 Vincenzo Librandi, <a href="/A130080/b130080.txt">Table of n, a(n) for n = 1..1000</a>
%F A130080 a(n) = ceiling(10^((n-1)/6)).
%e A130080 6^6 = 46656 has five digits, 7^6 = 117649 has six digits, hence a(6) = 7.
%t A130080 Table[(Ceiling[10^((n - 1)/6)]), {n, 1, 100}] (* _Vincenzo Librandi_, Sep 20 2013 *)
%o A130080 (Magma) [ Ceiling(Root(10^(n-1),6)): n in [1..41] ];
%o A130080 (Python)
%o A130080 from sympy import integer_nthroot
%o A130080 def A130080(n):
%o A130080     a, b = integer_nthroot(10**(n-1),6)
%o A130080     return a+(not b) # _Chai Wah Wu_, Jun 19 2024
%Y A130080 Cf. 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), A130081 to A130084 (smallest number whose seventh ... tenth power has n digits).
%K A130080 nonn,base,easy
%O A130080 1,2
%A A130080 _Klaus Brockhaus_, May 07 2007