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A183082 Tree generated by the Beatty sequence of 4-sqrt(6).

%I A183082 #10 Nov 09 2015 15:57:09
%S A183082 1,2,3,5,4,8,7,14,6,11,12,22,10,19,21,39,9,16,17,30,18,33,34,61,15,28,
%T A183082 29,53,32,59,60,109,13,25,24,45,26,47,46,84,27,50,51,92,52,95,94,171,
%U A183082 23,42,43,78,44,81,82,149,49,90,91,166,93,168,169,306,20
%N A183082 Tree generated by the Beatty sequence of 4-sqrt(6).
%C A183082 A permutation of the positive integers.
%H A183082 Ivan Neretin, <a href="/A183082/b183082.txt">Table of n, a(n) for n = 1..8192</a>
%H A183082 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A183082 Let L(n)=floor(r*n) and U(n)=floor(s*n), where r=4-sqrt(6) and s=r/(r-1).
%F A183082 The tree-array T(n,k) is then given by rows:
%F A183082 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);
%F A183082 for j=0,1,...,2^(n-1)-1, n>=2.
%e A183082 The top five rows:
%e A183082 1
%e A183082 2
%e A183082 3 5
%e A183082 4 8 7 14
%e A183082 6 11 12 22 10 19 21 39
%t A183082 a = {1, 2}; row = {a[[-1]]}; r = 4 - Sqrt[6]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* _Ivan Neretin_, Nov 09 2015 *)
%Y A183082 Cf. A074049, A183079.
%K A183082 nonn
%O A183082 1,2
%A A183082 _Clark Kimberling_, Dec 23 2010