%I #19 Sep 08 2022 08:44:44

%S 1,2,3,3,5,7,9,13,19,27,39,57,81,117,169,243,351,506,729,1052,1517,

%T 2187,3155,4550,6561,9463,13648,19683,28388,40943,59049,85164,122827,

%U 177147,255491,368481,531441,766471,1105442,1594323,2299412,3316326,4782969,6898235

%N Powers of cube root of 3 rounded up.

%C Smallest integer such that a(n)^k-k^n is nonnegative for all nonnegative integers k. - _Henry Bottomley_, May 16 2005

%H Vincenzo Librandi, <a href="/A017984/b017984.txt">Table of n, a(n) for n = 0..200</a>

%t Table[Ceiling[3^(n/3)], {n, 0, 50}] (* _Vincenzo Librandi_, Jan 09 2014 *)

%o (Magma) [Ceiling(3^(n/3)): n in [0..50]]; // _Vincenzo Librandi_, Jan 09 2014

%o (PARI) a(n)=ceil(3^(n/3)) \\ _Charles R Greathouse IV_, Jan 09 2014

%Y Cf. A107586 and powers of cube root of k ceiling up: A017981 (k=2), this sequence (k=3), A017987 (k=4), A017990 (k=5), A017993 (k=6), A017996 (k=7), A018002 (k=9), A018005 (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

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Jan 09 2014