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

Author

Paul Tek, Oct 04 2013

Keywords

• nonn
• look

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)

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.

Examples

			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.
		

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

Crossrefs

Cf. A046959, A046964, A229976.

Programs

Perl

See Links section.

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