A059556 - OEIS

%I #21 Jan 03 2016 14:12:41

%S 2,5,8,10,13,16,19,21,24,27,30,32,35,38,40,43,46,49,51,54,57,60,62,65,

%T 68,71,73,76,79,81,84,87,90,92,95,98,101,103,106,109,112,114,117,120,

%U 122,125,128,131,133,136,139,142,144,147,150,153,155,158,161,163,166

%N Beatty sequence for 1 + 1/gamma.

%C Differs from A054088 at indices 56, 71, 112, 127, 142, 168, 183 etc. - _R. J. Mathar_, Oct 05 2008

%C Let r = gamma (the Euler constant, 0.5772...). When {k*r, k >= 1} is jointly ranked with the positive integers, A059555(n) is the position of n and A059556(n) is the position of n*r. - _Clark Kimberling_, Oct 21 2014

%H Harry J. Smith, <a href="/A059556/b059556.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>

%t t = N[Table[k*EulerGamma, {k, 1, 200}]]; u = Union[Range[200], t]

%t Flatten[Table[Flatten[Position[u, n]], {n, 1, 100}]]  (* A059556 *)

%t Flatten[Table[Flatten[Position[u, t[[n]]]], {n, 1, 100}]] (* A059555 *)

%t (* _Clark Kimberling_, Oct 21 2014 *)

%o (PARI) { default(realprecision, 100); b=1 + 1/Euler; for (n = 1, 2000, write("b059556.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 28 2009

%Y Beatty complement is A059555.

%K nonn,easy

%O 1,1

%A _Mitch Harris_, Jan 22 2001