A228784 Permutation of the positive integers related to the "Sine tree" (see Comments lines for construction details).

1, 3, 2, 4, 8, 9, 5, 7, 10, 18, 16, 37, 21, 15, 43, 75, 33, 36, 20, 14, 11, 19, 17, 34, 38, 22, 29, 41, 73, 66, 150, 86, 31, 172, 300, 132, 147, 83, 59, 44, 76, 68, 35, 39, 6, 13, 79, 71, 136, 152, 88, 119, 167, 295, 264, 600, 344, 62, 173, 301, 133, 146, 82

Offset

1,2

Comments

The "Sine tree" is constructed according to this procedure:

take an infinite complete binary tree,

initially, the nodes have no value,

for each n=1,2,3,...:

move to the root node,

while the current node has a value:

if sin(n)<sin(node.value) then move to the left child node,

else move to the right child node.

assign the value n to the current node.

As the set {sin(1), sin(2), sin(3), ...} is dense in the open interval ]-1, +1[, each node will eventually have a value.

a(n) corresponds to the "index" of the node with value n:

- the index of the root node is 1,

- the index of the left child of the node with index k is 2*k,

- the index of the right child of the node with index k is 2*k+1.

a(A046959(n)) = 2^(n-1)-1, for any n>1.

a(A046964(n)) = 2^(n-1), for any n>0.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, The 7 first nodes of the Sine tree

Paul Tek, Perl program for this sequence

Index entries for sequences that are permutations of the natural numbers

Example

For n=1: the root node has no value, so we assign it the value 1, and a(1)=1.
For n=2: the root node has value 1, and sin(2)>sin(1), so we move to the right child node. This node has no value, so we assign it the value 2, and a(2)=2*1+1.
For n=3: the root node has value 1, and sin(3)<sin(1), so we move to the left child node. This node has no value, so we assign it the value 3, and a(3)=2*1.

Prog

(Perl) See Links section.

Crossrefs

Cf. A046959, A046964, A229976.

Sequence in context: A276953 A276943 A303148 * A082328 A082327 A072798

Adjacent sequences: A228781 A228782 A228783 * A228785 A228786 A228787

Keyword

nonn,look

Author

Paul Tek, Oct 04 2013

Status

approved