%I #11 Nov 10 2015 07:18:32
%S 1,2,3,5,4,8,7,13,6,10,12,21,11,18,20,35,9,16,15,27,19,32,33,56,17,29,
%T 28,48,31,54,55,94,14,24,25,43,23,40,42,73,30,51,50,86,52,89,88,151,
%U 26,46,45,78,44,75,76,129,49,83,85,146,87,148,149,254
%N Tree generated by the Beatty sequence of 3-sqrt(2).
%C A permutation of the positive integers. See the note at A183079.
%H Ivan Neretin, <a href="/A183080/b183080.txt">Table of n, a(n) for n = 1..8192</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F Let L(n)=floor(n*r), U(n)=floor(n*s), where r=3-sqrt(2) and s=r/(r-1).
%F The tree-array T(n,k) is then given by rows: T(0,0) = 1; T(1,0) = 2; T(n,2j) = L(T(n-1),j); T(n,2j+1) = U(T(n-1),j); for j=0,1,...,2^(n-1)-1, n>=2.
%e First five rows:
%e 1
%e 2
%e 3 5
%e 4 8 7 13
%e 6 10 12 21 11 18 20 35
%t a = {1, 2}; row = {a[[-1]]}; r = 3 - Sqrt[2]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* _Ivan Neretin_, Nov 09 2015 *)
%Y Cf. A183079, A178528, A074049.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Dec 23 2010