A017984 Powers of cube root of 3 rounded up.

1, 2, 3, 3, 5, 7, 9, 13, 19, 27, 39, 57, 81, 117, 169, 243, 351, 506, 729, 1052, 1517, 2187, 3155, 4550, 6561, 9463, 13648, 19683, 28388, 40943, 59049, 85164, 122827, 177147, 255491, 368481, 531441, 766471, 1105442, 1594323, 2299412, 3316326, 4782969, 6898235

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Smallest integer such that a(n)^k-k^n is nonnegative for all nonnegative integers k. - Henry Bottomley, May 16 2005

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

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).

Programs

Magma

[Ceiling(3^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 09 2014

Mathematica

Table[Ceiling[3^(n/3)], {n, 0, 50}] (* Vincenzo Librandi, Jan 09 2014 *)

PARI

a(n)=ceil(3^(n/3)) \\ Charles R Greathouse IV, Jan 09 2014

Extensions

More terms from Vincenzo Librandi, Jan 09 2014