A183211 First of two trees generated by floor[(3n-1)/2].

1, 3, 4, 9, 5, 12, 13, 27, 7, 15, 17, 36, 19, 39, 40, 81, 10, 21, 22, 45, 25, 51, 53, 108, 28, 57, 58, 117, 59, 120, 121, 243, 14, 30, 31, 63, 32, 66, 67, 135, 37, 75, 76, 153, 79, 159, 161, 324, 41, 84, 85, 171, 86, 174, 175, 351, 88, 177

Offset: 1

Author

Clark Kimberling, Dec 30 2010

Keywords

• nonn

Comments

This tree grows from (L(1),U(1))=(1,3). The second tree, A183212, grows from (L(2),U(2))=(2,6). Here, L(n)=floor[(3n-1)/2] and U(n)=3n. The two trees are complementary in the sense that every positive integer is in exactly one tree. The sequence formed by taking the terms of this tree in increasing order is A183213. Leftmost branch of this tree: A183207. Rightmost: A000244. See A183170 and A183171 for the two trees generated by the Beatty sequence of sqrt(2).

Examples

			First four levels of the tree:
.......................1
.......................3
..............4..................9
............5...12............13....27
		

Links

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

Crossrefs

Cf. A183170, A183212, A001651, A008585, A183209, A183213.

Programs

Mathematica

a = {1, 3}; row = {a[[-1]]}; Do[a = Join[a, row = Flatten[{Quotient[3 # - 1, 2], 3 #} & /@ row]], {n, 5}]; a (* Ivan Neretin, May 25 2015 *)

Formula

See the formula at A183209, but use L(n)=floor[(3n-1)/2] and U(n)=3n instead of L(n)=floor(3n/2) and U(n)=3n-1.