A018005 Smallest number whose cube has n digits.

1, 3, 5, 10, 22, 47, 100, 216, 465, 1000, 2155, 4642, 10000, 21545, 46416, 100000, 215444, 464159, 1000000, 2154435, 4641589, 10000000, 21544347, 46415889, 100000000, 215443470, 464158884, 1000000000, 2154434691, 4641588834

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

With offset 0, ((cube root of 10) to the power n) rounded up.

From Carmine Suriano, Mar 14 2020: (Start)

The terms corresponding to n = (20,21); (38,39); (41,42); (56,57); (59,60); (77,78); (80,81) ... are such that the square of first term starts with the digits of second term, and the square of second term starts with the digits of the first. For example, a(38)^2 = 2154434690032^2 = 4641588833613.... and a(39)^2 = 4641588833613^2 = 2154434690032...

(End)

Examples

			a(5) = 22, 22^3 = 10648 has 5 digits, while 21^3 = 9261 has 4 digits.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A061434, A061439, and powers of cube root of k ceiling up: A017981 (k=2), A017984 (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), this sequence (k=10), A018008 (k=11), A018011 (k=12), A018014 (k=13), A018017 (k=14), A018020 (k=15), A018023 (k=16), A018026 (k=17), A018029 (k=18), A018032 (k=19), A018035 (k=20), A018038 (k=21), A018041 (k=22), A018044 (k=23), A018047 (k=24).

Programs

Magma

[Ceiling(10^(n/3)): n in [0..40]]; // Vincenzo Librandi, Jan 09 2014

Mathematica

Table[Ceiling[10^(n/3)], {n, 0, 40}] (* Vincenzo Librandi, Jan 09 2014 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 16 2001