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A183171 Second of two trees generated by the Beatty sequence of sqrt(2).

%I A183171 #15 May 25 2015 15:36:07
%S A183171 2,6,8,20,11,27,28,68,15,37,38,92,39,95,96,232,21,51,52,126,53,129,
%T A183171 130,314,55,133,134,324,135,327,328,792,29,71,72,174,73,177,178,430,
%U A183171 74,180,182,440,183,443,444,1072,77,187,188
%N A183171 Second of two trees generated by the Beatty sequence of sqrt(2).
%C A183171 This tree grows from (L(2),U(2))=(2,6).  The other tree grows from (L(1),U(1))=(1,3).  Here, L and U are Beatty sequences.  See the comments at A183170 and A183173.
%H A183171 Ivan Neretin, <a href="/A183171/b183171.txt">Table of n, a(n) for n = 1..8192</a>
%F A183171 (See A183170.)
%e A183171 First levels of the tree:
%e A183171 .......................2
%e A183171 .......................6
%e A183171 ...............8.................20
%e A183171 ..........11.......27........28.......68
%e A183171 ........15..37...38..92....39..95...96..232
%t A183171 a = {2, 6}; row = {a[[-1]]}; r = Sqrt[2]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* _Ivan Neretin_, May 25 2015 *)
%Y A183171 Cf. A183170, A183173.
%K A183171 nonn,tabf
%O A183171 1,1
%A A183171 _Clark Kimberling_, Dec 28 2010