A130084 Smallest number whose tenth power has at least n digits.

1, 2, 2, 2, 3, 4, 4, 6, 7, 8, 10, 13, 16, 20, 26, 32, 40, 51, 64, 80, 100, 126, 159, 200, 252, 317, 399, 502, 631, 795, 1000, 1259, 1585, 1996, 2512, 3163, 3982, 5012, 6310, 7944, 10000, 12590, 15849, 19953, 25119, 31623, 39811, 50119, 63096, 79433, 100000

Offset: 1

Author

Klaus Brockhaus, May 07 2007

Keywords

• nonn
• base
• easy

Comments

Powers of tenth root of 10 rounded up.

Examples

			3^10 = 59049 has five digits, 4^10 = 1048576 has seven digits, hence a(6) = a(7) = 4.
		

Links

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

Crossrefs

Cf. A011279, 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 A130083 (smallest number whose sixth ... ninth power has n digits).

Programs

Magma

[Ceiling(Root(10^(n-1),10)): n in [1..51]];

Mathematica

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

Python

from sympy import integer_nthroot
def A130084(n): return (lambda x:x[0]+(not x[1]))(integer_nthroot(10**(n-1),10)) # Chai Wah Wu, Jun 20 2024

Formula

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