A183080 Tree generated by the Beatty sequence of 3-sqrt(2).

1, 2, 3, 5, 4, 8, 7, 13, 6, 10, 12, 21, 11, 18, 20, 35, 9, 16, 15, 27, 19, 32, 33, 56, 17, 29, 28, 48, 31, 54, 55, 94, 14, 24, 25, 43, 23, 40, 42, 73, 30, 51, 50, 86, 52, 89, 88, 151, 26, 46, 45, 78, 44, 75, 76, 129, 49, 83, 85, 146, 87, 148, 149, 254

Offset: 1

Author

Clark Kimberling, Dec 23 2010

Keywords

• nonn
• tabf

Comments

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

Examples

			First five rows:
1
2
3 5
4 8 7 13
6 10 12 21 11 18 20 35
		

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. A183079, A178528, A074049.

Programs

Mathematica

a = {1, 2}; row = {a[[-1]]}; r = 3 - Sqrt[2]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* Ivan Neretin, Nov 09 2015 *)

Formula

Let L(n)=floor(n*r), U(n)=floor(n*s), where r=3-sqrt(2) 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) = L(T(n-1),j); T(n,2j+1) = U(T(n-1),j); for j=0,1,...,2^(n-1)-1, n>=2.