cp's OEIS Frontend

A001955 Beatty sequence of 1 + 1/sqrt(11).

%I A001955 M0615 N0225 #28 Jul 30 2024 04:19:41
%S A001955 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 A001955 33,35,36,37,39,40,41,42,44,45,46,48,49,50,52,53,54,55,57,58,59,61,62,
%U A001955 63,65,66,67,68,70,71,72,74,75,76,78,79,80,81,83,84,85,87,88
%N A001955 Beatty sequence of 1 + 1/sqrt(11).
%C A001955 From _R. J. Mathar_, Feb 12 2011: (Start)
%C A001955 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 A001955 According to the Fraenkel article, the complementary sequence is defined by floor(n*(1+sqrt(11))). (End)
%D A001955 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001955 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001955 T. D. Noe, <a href="/A001955/b001955.txt">Table of n, a(n) for n = 1..10000</a>
%H A001955 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 A001955 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 A001955 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%p A001955 A001955 := proc(n) local x ; x := 1+1/sqrt(11) ; floor(n*x) ; end proc:
%p A001955 # for the complementary sequence
%p A001955 A001955compl := proc(n) local x ; x := 1+sqrt(11) ; floor(n*x) ; end proc:
%p A001955 seq(A001955(n),n=1..100) ; # _R. J. Mathar_, Feb 12 2011
%t A001955 Table[Floor[n*(1 + 1/Sqrt[11])], {n, 1, 65}]
%K A001955 nonn
%O A001955 1,2
%A A001955 _N. J. A. Sloane_
%E A001955 More terms from _Robert G. Wilson v_, Nov 02 2000