%I #31 Sep 08 2022 08:44:44

%S 1,3,5,10,22,47,100,216,465,1000,2155,4642,10000,21545,46416,100000,

%T 215444,464159,1000000,2154435,4641589,10000000,21544347,46415889,

%U 100000000,215443470,464158884,1000000000,2154434691,4641588834

%N Smallest number whose cube has n digits.

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

%C From _Carmine Suriano_, Mar 14 2020: (Start)

%C 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...

%C (End)

%H Vincenzo Librandi, <a href="/A018005/b018005.txt">Table of n, a(n) for n = 1..200</a>

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

%t Table[Ceiling[10^(n/3)], {n, 0, 40}] (* _Vincenzo Librandi_, Jan 09 2014 *)

%o (Magma) [Ceiling(10^(n/3)): n in [0..40]]; // _Vincenzo Librandi_, Jan 09 2014

%Y 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).

%K nonn,base,easy

%O 1,2

%A _N. J. A. Sloane_

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