

A183170


First of two trees generated by the Beatty sequence of sqrt(2).


5



1, 3, 4, 10, 5, 13, 14, 34, 7, 17, 18, 44, 19, 47, 48, 116, 9, 23, 24, 58, 25, 61, 62, 150, 26, 64, 66, 160, 67, 163, 164, 396, 12, 30, 32, 78, 33, 81, 82, 198, 35, 85, 86, 208, 87, 211, 212, 512, 36, 88, 90, 218, 93, 225, 226, 546, 94, 228
(list;
graph;
refs;
listen;
history;
text;
internal format)



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/(r1). 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



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



STATUS

approved



