A183081 Tree generated by the Beatty sequence of 4-sqrt(5).

1, 2, 3, 4, 5, 6, 7, 9, 8, 11, 10, 13, 12, 16, 15, 20, 14, 18, 19, 25, 17, 23, 22, 30, 21, 27, 28, 36, 26, 34, 35, 46, 24, 32, 31, 41, 33, 43, 44, 57, 29, 39, 40, 53, 38, 50, 52, 69, 37, 48, 47, 62, 49, 64, 63, 83, 45, 60, 59, 78, 61, 80, 81

Offset

1,2

Comments

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

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(n*r), U(n)=floor(n*s), where r=4-sqrt(5) 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

Top 5 rows:
1
2
3 4
5 6 7 9
8 11 10 13 12 16 15 20

Mathematica

a = {1, 2}; row = {a[[-1]]}; r = 4 - Sqrt[5]; 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, A178528, A183079.

Sequence in context: A180198 A180199 A284120 * A140595 A187098 A187099

Adjacent sequences: A183078 A183079 A183080 * A183082 A183083 A183084

Keyword

nonn,tabf

Author

Clark Kimberling, Dec 23 2010

Status

approved