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

1,2

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).

Links

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

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.

Example

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

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 *)

Crossrefs

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

Sequence in context: A070154 A331025 A330403 * A256469 A192334 A140439

Adjacent sequences: A183208 A183209 A183210 * A183212 A183213 A183214

Keyword

nonn

Author

Clark Kimberling, Dec 30 2010

Status

approved