A178528 Tree generated by the Beatty sequence of sqrt(3).

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, 24, 33, 25, 35, 36, 49, 22, 30, 31, 42, 32, 44, 45, 61, 34, 47, 48, 66, 46, 63, 64, 87, 29, 40, 39, 54, 41, 56, 57, 78, 43, 59, 60, 82, 62, 85, 84, 115

Offset: 1

Author

Clark Kimberling, Dec 23 2010

Keywords

• nonn
• tabf

Comments

A permutation of the positive integers.

Examples

			First levels of the tree:
.....................1
.....................2
..............3..............4
..........5.......7......6.......9
........8..11..12..16..10..14..15..21
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

Mathematica

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 *)

Formula

Let r=sqrt(3) and s=r/(r-1). The tree-array T(n,k) is then

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

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

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

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