A183082 Tree generated by the Beatty sequence of 4-sqrt(6).

1, 2, 3, 5, 4, 8, 7, 14, 6, 11, 12, 22, 10, 19, 21, 39, 9, 16, 17, 30, 18, 33, 34, 61, 15, 28, 29, 53, 32, 59, 60, 109, 13, 25, 24, 45, 26, 47, 46, 84, 27, 50, 51, 92, 52, 95, 94, 171, 23, 42, 43, 78, 44, 81, 82, 149, 49, 90, 91, 166, 93, 168, 169, 306, 20

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 L(n)=floor(r*n) and U(n)=floor(s*n), where r=4-sqrt(6) 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.

Example

The top five rows:
1
2
3 5
4 8 7 14
6 11 12 22 10 19 21 39

Mathematica

a = {1, 2}; row = {a[[-1]]}; r = 4 - Sqrt[6]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* Ivan Neretin, Nov 09 2015 *)

Crossrefs

Cf. A074049, A183079.

Sequence in context: A096070 A075157 A183080 * A183209 A046708 A338251

Adjacent sequences: A183079 A183080 A183081 * A183083 A183084 A183085

Keyword

nonn

Author

Clark Kimberling, Dec 23 2010

Status

approved