A295895 Parity of the binary weight of the contents of node n in Doudna-tree (A005940).

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

Offset

0

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) = A000035(A295894(n)) = A010060(A005940(1+n)).

a(0) = 1; after which, a(2n+1) = a(n), a(2n) = a(n) + A295893(n) mod 2.

a(n) = A295875(n) + A295896(n) mod 2.

If n is even and A295896(n) = 1 [i.e., when n is even and A005940(1+n) is a square], then a(n) = A010059(A292602(n)).

Example

The first six levels of the binary tree (compare also to the illustrations given at A005940, A295894 and A295875):
                               1
                               |
                               1
                ............../ \..............
               0                               1
        ....../ \......                 ....../ \......
       0               0               0               1
      / \             / \             / \             / \
     /   \           /   \           /   \           /   \
    1     0         0     0         1     0         0     1
   / \   / \       / \   / \       / \   / \       / \   / \
  1   1 1   0     1   0 0   0     1   1 0   0     0   0 1   1

Prog

(Scheme) (definec (A295895 n) (cond ((zero? n) 1) ((odd? n) (A295895 (/ (- n 1) 2))) (else (A000035 (+ (A295893 (/ n 2)) (A295895 (/ n 2)))))))

Crossrefs

Cf. A000035, A005940, A010059, A010060, A292602, A295875, A295893, A295894.

Cf. also A292583, A295296, A295297, A295298.

Sequence in context: A214529 A113681 A356163 * A179416 A360845 A155972

Adjacent sequences: A295892 A295893 A295894 * A295896 A295897 A295898

Keyword

nonn

Author

Antti Karttunen, Nov 30 2017

Status

approved