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

1, 2, 2, 3, 4, 6, 8, 10, 14, 20, 27, 38, 52, 72, 100, 139, 194, 269, 373, 518, 720, 1000, 1390, 1931, 2683, 3728, 5180, 7197, 10000, 13895, 19307, 26827, 37276, 51795, 71969, 100000, 138950, 193070, 268270, 372760, 517948, 719686, 1000000, 1389496

Offset: 1

Author

Klaus Brockhaus, May 07 2007

Keywords

• nonn
• base
• easy

Comments

Powers of seventh root of 10 rounded up.

Examples

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

Links

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

Crossrefs

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).

Programs

Magma

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

Mathematica

Table[(Ceiling[10^((n - 1)/7)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 20 2013 *)

Python

from sympy import integer_nthroot
def A130081(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),7)) # Chai Wah Wu, Jun 20 2024

Formula

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