A059551 - OEIS

%I #27 Aug 16 2024 23:11:49

%S 2,5,8,10,13,16,18,21,24,26,29,32,34,37,40,42,45,48,50,53,56,58,61,64,

%T 66,69,72,75,77,80,83,85,88,91,93,96,99,101,104,107,109,112,115,117,

%U 120,123,125,128,131,133,136,139,141,144,147,150,152,155,158,160,163

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

%H Harry J. Smith, <a href="/A059551/b059551.txt">Table of n, a(n) for n = 1..2000</a>

%H Aviezri S. Fraenkel, Jonathan Levitt, 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(1/3)). - _Michel Marcus_, Jan 04 2015

%t Table[Floor[n Gamma[1/3]], {n, 70}] (* _Vincenzo Librandi_, Jan 07 2015 *)

%o (PARI) { default(realprecision, 100); b=gamma(1/3); for (n = 1, 2000, write("b059551.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 28 2009

%o (Magma) [Floor(n*Gamma(1/3)): n in [1..80]]; // _Vincenzo Librandi_, Jan 07 2015

%Y Beatty complement is A059552.

%Y Cf. A073005 (Gamma(1/3)).

%K nonn,easy

%O 1,1

%A _Mitch Harris_, Jan 22 2001