A252744 a(n) = A252742(A163511(n)).

0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1

Offset

0

Comments

a(n) is 1 if the n-th node in A163511 (starting offset 0) has a pair of children where the left child is smaller than the right child, otherwise zero.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Formula

a(n) = A252742(A163511(n)).

a(n) = A252743(A054429(n)). [The tree is a mirror image of the tree of A252743.]

Example

The first six levels of the binary tree (compare also to the illustration given at A163511):
                               0
                               |
                               0
                ............../ \..............
               1                               0
        ....../ \......                 ....../ \......
       1               1               1               0
      / \             / \             / \             / \
     /   \           /   \           /   \           /   \
    1     1         1     0         1     1         1     0
   / \   / \       / \   / \       / \   / \       / \   / \
  1   1 1   1     1   1 1   1     1   1 1   1     1   1 1   0
For n=0, the corresponding node in A163511(0) is 1, which has just one child 2, thus we set a(0) = 0.
For n=1, the corresponding node in A163511(1) is 2, which has children 4 > 3, with left child not less than the right child, thus a(1) = 0.
On the other hand, for node 4, in position 3, with its children 8 < 9, thus a(2) = 1. But for node 3, in position 4, with its children 6 > 5, we set a(4) = 0.

Prog

(Scheme) (define (A252744 n) (A252742 (A163511 n)))

Crossrefs

Cf. A163511, A003961, A048673.

Permutations: A252742, A252743.

Cf. A252745 (number of ones) and A252746 (number of zeros on each level of binary tree).

Sequence in context: A011656 A295309 A353670 * A340373 A043545 A094754

Adjacent sequences: A252741 A252742 A252743 * A252745 A252746 A252747

Keyword

nonn,tabf

Author

Antti Karttunen, Dec 21 2014

Status

approved