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%I #12 Nov 09 2015 13:10:27
%S 1,2,3,4,5,7,6,9,8,11,12,16,10,14,15,21,13,19,18,26,20,28,27,38,17,23,
%T 24,33,25,35,36,50,22,31,32,45,30,43,44,62,34,47,48,66,46,64,65,90,29,
%U 40,39,55,41,57,56,78,42,59,60,83,61,86,85,119
%N Tree generated by the Beatty sequence of e-1.
%C A permutation of the positive integers.
%H Ivan Neretin, <a href="/A183084/b183084.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(r*n) and U(n) = floor(s*n), where r=e-1 and s=r/(r-1).
%F The tree-array T(n,k) is then given by rows:
%F 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 for j=0,1,...,2^(n-1)-1, n>=2.
%e Top 5 rows:
%e 1
%e 2
%e 3 4
%e 5 7 6 9
%e 8 11 12 16 10 14 15 21
%t a = {1, 2}; row = {a[[-1]]}; r = E - 1; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* _Ivan Neretin_, Nov 09 2015 *)
%Y Cf. A074049, A183079.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Dec 23 2010
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