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A183081 Tree generated by the Beatty sequence of 4-sqrt(5). 1

%I #11 Nov 09 2015 15:57:39

%S 1,2,3,4,5,6,7,9,8,11,10,13,12,16,15,20,14,18,19,25,17,23,22,30,21,27,

%T 28,36,26,34,35,46,24,32,31,41,33,43,44,57,29,39,40,53,38,50,52,69,37,

%U 48,47,62,49,64,63,83,45,60,59,78,61,80,81

%N Tree generated by the Beatty sequence of 4-sqrt(5).

%C A permutation of the positive integers. See the note at A183079.

%H Ivan Neretin, <a href="/A183081/b183081.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(n*r), U(n)=floor(n*s), where r=4-sqrt(5) 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 6 7 9

%e 8 11 10 13 12 16 15 20

%t a = {1, 2}; row = {a[[-1]]}; r = 4 - Sqrt[5]; 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, A178528, A183079.

%K nonn,tabf

%O 1,2

%A _Clark Kimberling_, Dec 23 2010

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)