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A295895 Parity of the binary weight of the contents of node n in Doudna-tree (A005940). 6
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 (list; graph; refs; listen; history; text; internal format)
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: A113430 A214529 A113681 * A179416 A155972 A010054

Adjacent sequences:  A295892 A295893 A295894 * A295896 A295897 A295898

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 30 2017

STATUS

approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)