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%I #10 Nov 09 2015 15:58:18
%S 1,2,3,4,5,6,7,8,9,11,10,13,12,15,14,17,16,19,20,24,18,22,23,28,21,26,
%T 27,33,25,30,31,37,29,35,34,41,36,44,43,52,32,39,40,48,42,50,51,61,38,
%U 46,47,57,49,59,60,72,45,55,54,66,56,68,67,81,53,64
%N Tree generated by the Beatty sequence of -1+sqrt(8).
%C A permutation of the positive integers.
%H Ivan Neretin, <a href="/A183083/b183083.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=-1+sqrt(8) 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 five rows:
%e 1
%e 2
%e 3 4
%e 5 6 7 8
%e 9 11 10 13 12 15 14 17
%t a = {1, 2}; row = {a[[-1]]}; r = Sqrt[8] - 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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