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

1, 2, 2, 3, 4, 5, 6, 8, 10, 14, 18, 24, 32, 43, 57, 75, 100, 134, 178, 238, 317, 422, 563, 750, 1000, 1334, 1779, 2372, 3163, 4217, 5624, 7499, 10000, 13336, 17783, 23714, 31623, 42170, 56235, 74990, 100000, 133353, 177828, 237138, 316228, 421697

Offset: 1

Author

Klaus Brockhaus, May 07 2007

Keywords

• nonn
• base
• easy

Comments

Powers of eighth root of 10 rounded up.

Examples

			9^8 = 43046721 has eight digits, 10^8 = 100000000 has nine digits, hence a(9) = 10.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

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).

Programs

Magma

[ Ceiling(Root(10^(n-1),8)): n in [1..46] ];

Mathematica

Table[(Ceiling[10^((n - 1)/8)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

Python

from sympy import integer_nthroot
def A130082(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),8)) # Chai Wah Wu, Jun 20 2024

Formula

a(n) = ceiling(10^((n-1)/8)).