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

1,2

Comments

Powers of seventh root of 10 rounded up.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

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), A130080 to A130084 (smallest number whose sixth ... tenth power has n digits).

Sequence in context: A066447 A035542 A225484 * A141847 A182372 A089333

Adjacent sequences: A130078 A130079 A130080 * A130082 A130083 A130084

Keyword

nonn,base,easy

Author

Klaus Brockhaus, May 07 2007

Status

approved