A059552 - OEIS

%I #27 Jul 05 2024 10:29:51

%S 1,3,4,6,7,9,11,12,14,15,17,19,20,22,23,25,27,28,30,31,33,35,36,38,39,

%T 41,43,44,46,47,49,51,52,54,55,57,59,60,62,63,65,67,68,70,71,73,74,76,

%U 78,79,81,82,84,86,87,89,90,92,94,95,97,98,100,102,103,105,106,108

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

%H Harry J. Smith, <a href="/A059552/b059552.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(1/3)/(Gamma(1/3)-1)). - _Michel Marcus_, Jan 04 2015

%t Floor[Range[100]*(1 + 1/(Gamma[1/3] - 1))] (* _Paolo Xausa_, Jul 05 2024 *)

%o (PARI) { default(realprecision, 100); b=gamma(1/3)/(gamma(1/3) - 1); for (n = 1, 2000, write("b059552.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 28 2009

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

%Y Beatty complement is A059551.

%Y Cf. A073005.

%K nonn,easy

%O 1,2

%A _Mitch Harris_, Jan 22 2001