

A178528


Tree generated by the Beatty sequence of sqrt(3).


5



1, 2, 3, 4, 5, 7, 6, 9, 8, 11, 12, 16, 10, 14, 15, 21, 13, 18, 19, 26, 20, 28, 27, 37, 17, 23, 24, 33, 25, 35, 36, 49, 22, 30, 31, 42, 32, 44, 45, 61, 34, 47, 48, 66, 46, 63, 64, 87, 29, 40, 39, 54, 41, 56, 57, 78, 43, 59, 60, 82, 62, 85, 84, 115
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OFFSET

1,2


COMMENTS

A permutation of the positive integers.


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers


FORMULA

Let r=sqrt(3) and s=r/(r1). The treearray T(n,k) is then
given by rows: T(0,0)=1; T(1,0)=2;
T(n,2j)=Floor(r*T(n1),j));
T(n,2j+1)=Floor((s*T(n1,j));
for j=0,1,...,2^(n1)1, n>=2.


EXAMPLE

First levels of the tree:
.....................1
.....................2
..............3..............4
..........5.......7......6.......9
........8..11..12..16..10..14..15..21


MATHEMATICA

a = {1, 2}; row = {a[[1]]}; r = Sqrt[3]; s = r/(r  1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* Ivan Neretin, Nov 09 2015 *)


CROSSREFS

Cf. A022838 (Beatty sequence of sqrt(3)), A054406, A074049.
Sequence in context: A209637 A120750 A265672 * A183084 A185975 A232639
Adjacent sequences: A178525 A178526 A178527 * A178529 A178530 A178531


KEYWORD

nonn,tabf


AUTHOR

Clark Kimberling, Dec 23 2010


STATUS

approved



