A295893 a(n) = 1 if in Doudna-tree (A005940) the contents of the node n and its left-hand child have binary weights with different parity, 0 otherwise.

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

Offset

0

Comments

Like A005940 and A252743 this can be viewed as a binary tree. See illustration below.

Links

Antti Karttunen, Table of n, a(n) for n = 0..16383

Index entries for sequences related to binary expansion of n

Index entries for characteristic functions

Index entries for sequences computed from indices in prime factorization

Formula

a(n) = A295891(A005940(1+n)).

a(n) = A000035(A295894(n) + A295894(2n)) = A295895(n) XOR A295895(2n).

Example

The first six levels of the binary tree (compare also to the illustrations given at A005940, A295894, A295895):
                               0
                               |
                               1
                ............../ \..............
               0                               1
        ....../ \......                 ....../ \......
       1               0               1               1
      / \             / \             / \             / \
     /   \           /   \           /   \           /   \
    0     1         1     0         0     0         0     0
   / \   / \       / \   / \       / \   / \       / \   / \
  0   1 0   0     1   0 0   0     0   1 0   0     0   1 0   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 by convention.
For n=1, the corresponding node in A005940(1+1) is 2, which has 3 as its left-hand child, and in binary 2 is "10", and 3 is "11", so the other one has an odd number of 1-bits, while the other has an even number of 1's, thus their parities differ and a(1) = 1.
For n=2, the corresponding node in A005940(1+2) is 3 (in binary "11"), which has 5 (in binary "101") as its left-hand child, and they have the same parity, thus a(2) = 0.
For n=3, the corresponding node in A005940(1+3) is 4 (in binary "100"), which has 9 (in binary "1001") as its left hand child, and here the parities differ, thus a(3) = 1.

Prog

(Scheme) (define (A295893 n) (A295891 (A005940 (+ 1 n))))

Crossrefs

Cf. A003961, A005940, A295891, A295894, A295895.

Cf. also A252743.

Sequence in context: A189301 A123640 A022924 * A157412 A023532 A226520

Adjacent sequences: A295890 A295891 A295892 * A295894 A295895 A295896

Keyword

nonn,tabf

Author

Antti Karttunen, Nov 30 2017

Status

approved