A178528 - OEIS

%I #16 Feb 09 2025 06:35:05

%S 1,2,3,4,5,7,6,9,8,11,12,16,10,14,15,21,13,18,19,26,20,28,27,37,17,23,

%T 24,33,25,35,36,49,22,30,31,42,32,44,45,61,34,47,48,66,46,63,64,87,29,

%U 40,39,54,41,56,57,78,43,59,60,82,62,85,84,115

%N Tree generated by the Beatty sequence of sqrt(3).

%C A permutation of the positive integers.

%H Ivan Neretin, <a href="/A178528/b178528.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 r=sqrt(3) and s=r/(r-1). The tree-array T(n,k) is then

%F given by rows: T(0,0)=1; T(1,0)=2;

%F T(n,2*j)=floor(r*T(n-1,j));

%F T(n,2*j+1)=floor(s*T(n-1,j));

%F for j=0,1,...,2^(n-1)-1, n>=2.

%e First levels of the tree:

%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 = Sqrt[3]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* _Ivan Neretin_, Nov 09 2015 *)

%Y Cf. A022838 (Beatty sequence of sqrt(3)), A054406, A074049.

%K nonn,tabf,changed

%O 1,2

%A _Clark Kimberling_, Dec 23 2010