A252743 a(n) = A252742(A005940(1+n)).

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

Offset

0

Comments

a(n) tells whether the n-th node in A005940 (here counted with offset 0) has a pair of children where the left child is larger than the right child, see illustration in A005940 and one below.

Links

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

Formula

a(n) = A252742(A005940(1+n)).

a(n) = A252744(A054429(n)). [The tree is a mirror image of the tree of A252744.]

Other identities. For all n >= 1:

sgn(A252750(n)) = (-1)^(1+a(n)).

Example

The first six levels of the binary tree (compare also to the illustration given at A005940):
                               0
                               |
                               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
For n=0, the corresponding node in A005940(0+1) is 1, which has just one child 2, thus we set a(0) = 0.
For n=1, the corresponding node in A005940(1+1) is 2, which has children 3 and 4, in correct order, thus a(1) = 0.
Similarly for node 3, with children 5 < 6, thus a(2) = 0. But for node 4, with its children 9 > 8, we set a(3) = 1.

Prog

(Scheme) (define (A252743 n) (A252742 (A005940 (+ 1 n))))

Crossrefs

Cf. A005940, A003961, A048673.

Permutations: A252742, A252744.

Cf. A252745 (number of ones) and A252746 (number of zeros on each level of binary tree), A252750, A252751.

Sequence in context: A169675 A093385 A350866 * A135136 A137331 A093386

Adjacent sequences: A252740 A252741 A252742 * A252744 A252745 A252746

Keyword

nonn,tabf

Author

Antti Karttunen, Dec 21 2014

Status

approved