login
A130083
Smallest number whose ninth power has at least n digits.
2
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
1,2
COMMENTS
Powers of ninth root of 10 rounded up.
LINKS
FORMULA
a(n) = ceiling(10^((n-1)/9)).
EXAMPLE
2^9 = 512 has three digits, 3^9 = 19683 has five digits, hence a(4) = a(5) = 3.
MATHEMATICA
Table[(Ceiling[10^((n - 1)/9)]), {n, 1, 60}] (* Vincenzo Librandi, Sep 21 2013 *)
PROG
(Magma) [ Ceiling(Root(10^(n-1), 9)): n in [1..49] ];
(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
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).
Sequence in context: A017980 A064650 A174619 * A369787 A363994 A286219
KEYWORD
nonn,base,easy
AUTHOR
Klaus Brockhaus, May 07 2007
STATUS
approved