

A183081


Tree generated by the Beatty sequence of 4sqrt(5).


1



1, 2, 3, 4, 5, 6, 7, 9, 8, 11, 10, 13, 12, 16, 15, 20, 14, 18, 19, 25, 17, 23, 22, 30, 21, 27, 28, 36, 26, 34, 35, 46, 24, 32, 31, 41, 33, 43, 44, 57, 29, 39, 40, 53, 38, 50, 52, 69, 37, 48, 47, 62, 49, 64, 63, 83, 45, 60, 59, 78, 61, 80, 81
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OFFSET

1,2


COMMENTS

A permutation of the positive integers. See the note at A183079.


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(n*r), U(n)=floor(n*s), where r=4sqrt(5) 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 5 rows:
1
2
3 4
5 6 7 9
8 11 10 13 12 16 15 20


MATHEMATICA

a = {1, 2}; row = {a[[1]]}; r = 4  Sqrt[5]; 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, A178528, A183079.
Sequence in context: A180198 A180199 A284120 * A140595 A187098 A187099
Adjacent sequences: A183078 A183079 A183080 * A183082 A183083 A183084


KEYWORD

nonn,tabf


AUTHOR

Clark Kimberling, Dec 23 2010


STATUS

approved



