A130081 - OEIS

%I #16 Jun 20 2024 14:47:10

%S 1,2,2,3,4,6,8,10,14,20,27,38,52,72,100,139,194,269,373,518,720,1000,

%T 1390,1931,2683,3728,5180,7197,10000,13895,19307,26827,37276,51795,

%U 71969,100000,138950,193070,268270,372760,517948,719686,1000000,1389496

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

%C Powers of seventh root of 10 rounded up.

%H Vincenzo Librandi, <a href="/A130081/b130081.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling(10^((n-1)/7)).

%e 1^7 = 1 has 1 digit, 2^7 = 128 has three digits, hence a(2) = a(3) = 2.

%t Table[(Ceiling[10^((n - 1)/7)]), {n, 1, 60}] (* _Vincenzo Librandi_, Sep 20 2013 *)

%o (Magma) [Ceiling(Root(10^(n-1),7)): n in [1..44]];

%o (Python)

%o from sympy import integer_nthroot

%o def A130081(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),7)) # _Chai Wah Wu_, Jun 20 2024

%Y 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 nonn,base,easy

%O 1,2

%A _Klaus Brockhaus_, May 07 2007