A183170 First of two trees generated by the Beatty sequence of sqrt(2).

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

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

Cf. A183171, A183172, A001951, A001952, A178528, A074049.

Sequence in context: A240546 A248003 A063930 * A014411 A247372 A143443

Adjacent sequences: A183167 A183168 A183169 * A183171 A183172 A183173

Keyword

nonn,tabf

Author

Clark Kimberling, Dec 28 2010

Status

approved