OFFSET
1,2
COMMENTS
This tree grows from (L(1),U(1))=(1,3). The other tree, A183171, grows from (L(2),U(2))=(2,6). Here, L is the Beatty sequence A001951 of r=sqrt(2); U is the Beatty sequence A001952 of s=r/(r-1). The two trees are complementary; that is, every positive integer is in exactly one tree. (L and U are complementary, too.) The sequence formed by taking the terms of this tree in increasing order is A183172.
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..8192
FORMULA
See the formula at A178528, but use r=sqrt(2) instead of r=sqrt(3).
EXAMPLE
First levels of the tree:
.......................1
.......................3
..............4...................10
.........5..........13........14........34
.......7..17......18..44....19..47....48..116
MATHEMATICA
a = {1, 3}; row = {a[[-1]]}; r = Sqrt[2]; s = r/(r - 1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* Ivan Neretin, May 25 2015 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Dec 28 2010
STATUS
approved