A059553 - OEIS

%I #27 Jul 05 2024 10:29:46

%S 1,2,4,5,6,8,9,10,12,13,14,16,17,18,20,21,23,24,25,27,28,29,31,32,33,

%T 35,36,37,39,40,41,43,44,46,47,48,50,51,52,54,55,56,58,59,60,62,63,64,

%U 66,67,69,70,71,73,74,75,77,78,79,81,82,83,85,86,88,89,90,92,93,94,96

%N Beatty sequence for Gamma(2/3).

%H Harry J. Smith, <a href="/A059553/b059553.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*Gamma(2/3)). - _Michel Marcus_, Jan 04 2015

%t Floor[Range[100]*Gamma[2/3]] (* _Paolo Xausa_, Jul 05 2024 *)

%o (PARI) { default(realprecision, 100); b=gamma(2/3); for (n = 1, 2000, write("b059553.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 28 2009

%o (Magma) [Floor(n*Gamma(2/3)): n in [1..80]]; // _Vincenzo Librandi_, Jan 06 2015

%Y Beatty complement is A059554.

%Y Cf. A073006 (Gamma(2/3)).

%K nonn,easy

%O 1,2

%A _Mitch Harris_, Jan 22 2001