A183084 Tree generated by the Beatty sequence of e-1.

1, 2, 3, 4, 5, 7, 6, 9, 8, 11, 12, 16, 10, 14, 15, 21, 13, 19, 18, 26, 20, 28, 27, 38, 17, 23, 24, 33, 25, 35, 36, 50, 22, 31, 32, 45, 30, 43, 44, 62, 34, 47, 48, 66, 46, 64, 65, 90, 29, 40, 39, 55, 41, 57, 56, 78, 42, 59, 60, 83, 61, 86, 85, 119

Offset: 1

Author

Clark Kimberling, Dec 23 2010

Keywords

• nonn
• tabf

Comments

A permutation of the positive integers.

Examples

			Top 5 rows:
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. A074049, A183079.

Programs

Mathematica

a = {1, 2}; row = {a[[-1]]}; r = E - 1; 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(r*n) and U(n) = floor(s*n), where r=e-1 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.