

A183083


Tree generated by the Beatty sequence of 1+sqrt(8).


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 13, 12, 15, 14, 17, 16, 19, 20, 24, 18, 22, 23, 28, 21, 26, 27, 33, 25, 30, 31, 37, 29, 35, 34, 41, 36, 44, 43, 52, 32, 39, 40, 48, 42, 50, 51, 61, 38, 46, 47, 57, 49, 59, 60, 72, 45, 55, 54, 66, 56, 68, 67, 81, 53, 64
(list;
graph;
refs;
listen;
history;
text;
internal format)



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=1+sqrt(8) 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

Top five rows:
1
2
3 4
5 6 7 8
9 11 10 13 12 15 14 17


MATHEMATICA

a = {1, 2}; row = {a[[1]]}; r = Sqrt[8]  1; 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: A239088 A162344 A283962 * A113220 A113218 A296424
Adjacent sequences: A183080 A183081 A183082 * A183084 A183085 A183086


KEYWORD

nonn,tabf


AUTHOR

Clark Kimberling, Dec 23 2010


STATUS

approved



