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A130081 Smallest number whose seventh power has at least n digits.

%I A130081 #16 Jun 20 2024 14:47:10
%S A130081 1,2,2,3,4,6,8,10,14,20,27,38,52,72,100,139,194,269,373,518,720,1000,
%T A130081 1390,1931,2683,3728,5180,7197,10000,13895,19307,26827,37276,51795,
%U A130081 71969,100000,138950,193070,268270,372760,517948,719686,1000000,1389496
%N A130081 Smallest number whose seventh power has at least n digits.
%C A130081 Powers of seventh root of 10 rounded up.
%H A130081 Vincenzo Librandi, <a href="/A130081/b130081.txt">Table of n, a(n) for n = 1..1000</a>
%F A130081 a(n) = ceiling(10^((n-1)/7)).
%e A130081 1^7 = 1 has 1 digit, 2^7 = 128 has three digits, hence a(2) = a(3) = 2.
%t A130081 Table[(Ceiling[10^((n - 1)/7)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 20 2013 *)
%o A130081 (Magma) [Ceiling(Root(10^(n-1),7)): n in [1..44]];
%o A130081 (Python)
%o A130081 from sympy import integer_nthroot
%o A130081 def A130081(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),7)) # _Chai Wah Wu_, Jun 20 2024
%Y A130081 Cf. A011276, 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 A130081 nonn,base,easy
%O A130081 1,2
%A A130081 _Klaus Brockhaus_, May 07 2007