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A252743
a(n) = A252742(A005940(1+n)).
9
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
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
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
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Dec 21 2014
STATUS
approved