A130083 Smallest number whose ninth power has at least n digits.

1, 2, 2, 3, 3, 4, 5, 6, 8, 10, 13, 17, 22, 28, 36, 47, 60, 78, 100, 130, 167, 216, 279, 360, 465, 600, 775, 1000, 1292, 1669, 2155, 2783, 3594, 4642, 5995, 7743, 10000, 12916, 16682, 21545, 27826, 35939, 46416, 59949, 77427, 100000, 129155, 166811, 215444

Offset: 1

Author

Klaus Brockhaus, May 07 2007

Keywords

• nonn
• base
• easy

Comments

Powers of ninth root of 10 rounded up.

Examples

			2^9 = 512 has three digits, 3^9 = 19683 has five digits, hence a(4) = a(5) = 3.
		

Links

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

Crossrefs

Cf. A011278, 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),9)): n in [1..49] ];

Mathematica

Table[(Ceiling[10^((n - 1)/9)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 21 2013 *)

Python

from sympy import integer_nthroot
def A130083(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),9)) # Chai Wah Wu, Jun 20 2024

Formula

a(n) = ceiling(10^((n-1)/9)).