

A183082


Tree generated by the Beatty sequence of 4sqrt(6).


1



1, 2, 3, 5, 4, 8, 7, 14, 6, 11, 12, 22, 10, 19, 21, 39, 9, 16, 17, 30, 18, 33, 34, 61, 15, 28, 29, 53, 32, 59, 60, 109, 13, 25, 24, 45, 26, 47, 46, 84, 27, 50, 51, 92, 52, 95, 94, 171, 23, 42, 43, 78, 44, 81, 82, 149, 49, 90, 91, 166, 93, 168, 169, 306, 20
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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 L(n)=floor(r*n) and U(n)=floor(s*n), where r=4sqrt(6) 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) = L(T(n1),j); T(n,2j+1) = U(T(n1),j);
for j=0,1,...,2^(n1)1, n>=2.


EXAMPLE

The top five rows:
1
2
3 5
4 8 7 14
6 11 12 22 10 19 21 39


MATHEMATICA

a = {1, 2}; row = {a[[1]]}; r = 4  Sqrt[6]; s = r/(r  1); Do[a = Join[a, row = Flatten[{Floor[#*{r, s}]} & /@ row]], {n, 5}]; a (* Ivan Neretin, Nov 09 2015 *)


CROSSREFS

Cf. A074049, A183079.
Sequence in context: A096070 A075157 A183080 * A183209 A046708 A185728
Adjacent sequences: A183079 A183080 A183081 * A183083 A183084 A183085


KEYWORD

nonn


AUTHOR

Clark Kimberling, Dec 23 2010


STATUS

approved



