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

1,2

Comments

A permutation of the positive integers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..8192

Index entries for sequences that are permutations of the natural numbers

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

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A347540 A120750 A265672 * A183084 A185975 A232639

Adjacent sequences: A178525 A178526 A178527 * A178529 A178530 A178531

Keyword

nonn,tabf

Author

Clark Kimberling, Dec 23 2010

Status

approved