%I M0615 N0225 #28 Jul 30 2024 04:19:41

%S 1,2,3,5,6,7,9,10,11,13,14,15,16,18,19,20,22,23,24,26,27,28,29,31,32,

%T 33,35,36,37,39,40,41,42,44,45,46,48,49,50,52,53,54,55,57,58,59,61,62,

%U 63,65,66,67,68,70,71,72,74,75,76,78,79,80,81,83,84,85,87,88

%N Beatty sequence of 1 + 1/sqrt(11).

%C From _R. J. Mathar_, Feb 12 2011: (Start)

%C The value of 1+1/sqrt(11) = 1.30151134457.. is close to (sqrt(13)-1)/2 = 1.3027756377..., so the early terms of the sequence are similar to A184480.

%C According to the Fraenkel article, the complementary sequence is defined by floor(n*(1+sqrt(11))). (End)

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001955/b001955.txt">Table of n, a(n) for n = 1..10000</a>

%H Ian G. Connell, <a href="http://dx.doi.org/10.4153/CMB-1959-024-3">A generalization of Wythoff's game</a>, Canad. Math. Bull. 2 (1959) 181-190

%H A. S. Fraenkel, <a href="http://www.jstor.org/stable/2321643">How to beat your Wythoff games' opponent on three fronts</a>, Amer. Math. Monthly, 89 (1982), 353-361.

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

%p A001955 := proc(n) local x ; x := 1+1/sqrt(11) ; floor(n*x) ; end proc:

%p # for the complementary sequence

%p A001955compl := proc(n) local x ; x := 1+sqrt(11) ; floor(n*x) ; end proc:

%p seq(A001955(n),n=1..100) ; # _R. J. Mathar_, Feb 12 2011

%t Table[Floor[n*(1 + 1/Sqrt[11])], {n, 1, 65}]

%K nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Robert G. Wilson v_, Nov 02 2000