A130080 Smallest number whose sixth power has n digits.

1, 2, 3, 4, 5, 7, 10, 15, 22, 32, 47, 69, 100, 147, 216, 317, 465, 682, 1000, 1468, 2155, 3163, 4642, 6813, 10000, 14678, 21545, 31623, 46416, 68130, 100000, 146780, 215444, 316228, 464159, 681293, 1000000, 1467800, 2154435, 3162278, 4641589

Offset: 1

Author

Klaus Brockhaus, May 07 2007

Keywords

• nonn
• base
• easy

Comments

Powers of sixth root of 10 rounded up.

Examples

			6^6 = 46656 has five digits, 7^6 = 117649 has six digits, hence a(6) = 7.
		

Links

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

Crossrefs

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).

Programs

Magma

[ Ceiling(Root(10^(n-1),6)): n in [1..41] ];

Mathematica

Table[(Ceiling[10^((n - 1)/6)]), {n, 1, 100}] (* Vincenzo Librandi, Sep 20 2013 *)

Python

from sympy import integer_nthroot
def A130080(n):
    a, b = integer_nthroot(10**(n-1),6)
    return a+(not b) # Chai Wah Wu, Jun 19 2024

Formula

a(n) = ceiling(10^((n-1)/6)).