%I #33 Jul 05 2024 07:49:38

%S 1,2,4,5,7,8,10,11,12,14,15,17,18,20,21,23,24,25,27,28,30,31,33,34,36,

%T 37,38,40,41,43,44,46,47,49,50,51,53,54,56,57,59,60,62,63,64,66,67,69,

%U 70,72,73,74,76,77,79,80,82,83,85,86,87,89,90,92,93,95,96,98,99,100

%N Beatty sequence for 3^(1/3).

%H Harry J. Smith, <a href="/A059539/b059539.txt">Table of n, a(n) for n = 1..2000</a>

%H Aviezri S. Fraenkel, Jonathan Levitt, and Michael Shimshoni, <a href="http://dx.doi.org/10.1016/0012-365X(72)90012-X">Characterization of the set of values f(n)=[n alpha], n=1,2,...</a>, Discrete Math. 2 (1972), no.4, 335-345.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F a(n) = floor(n*A002581). - _R. J. Mathar_, Apr 12 2019

%t Floor[Range[100]*CubeRoot[3]] (* _Paolo Xausa_, Jul 05 2024 *)

%o (PARI) { default(realprecision, 100); b=3^(1/3); for (n = 1, 2000, write("b059539.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 27 2009

%o (Python)

%o from sympy import integer_nthroot

%o def A059539(n): return integer_nthroot(3*n**3,3)[0] # _Chai Wah Wu_, Mar 16 2021

%Y Beatty complement is A059540.

%Y Partial sums of A081129.

%Y Cf. A002581.

%K nonn,easy

%O 1,2

%A _Mitch Harris_, Jan 22 2001