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A183084 Tree generated by the Beatty sequence of e-1.

%I A183084 #12 Nov 09 2015 13:10:27
%S A183084 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 A183084 24,33,25,35,36,50,22,31,32,45,30,43,44,62,34,47,48,66,46,64,65,90,29,
%U A183084 40,39,55,41,57,56,78,42,59,60,83,61,86,85,119
%N A183084 Tree generated by the Beatty sequence of e-1.
%C A183084 A permutation of the positive integers.
%H A183084 Ivan Neretin, <a href="/A183084/b183084.txt">Table of n, a(n) for n = 1..8192</a>
%H A183084 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A183084 Let L(n) = floor(r*n) and U(n) = floor(s*n), where r=e-1 and s=r/(r-1).
%F A183084 The tree-array T(n,k) is then given by rows:
%F A183084 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 A183084 for j=0,1,...,2^(n-1)-1, n>=2.
%e A183084 Top 5 rows:
%e A183084 1
%e A183084 2
%e A183084 3 4
%e A183084 5 7 6 9
%e A183084 8 11 12 16 10 14 15 21
%t A183084 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 A183084 Cf. A074049, A183079.
%K A183084 nonn,tabf
%O A183084 1,2
%A A183084 _Clark Kimberling_, Dec 23 2010