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A295894 Binary weight of the contents of node n in Doudna-tree (A005940). 4
1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 4, 2, 3, 2, 4, 1, 3, 3, 3, 2, 3, 4, 4, 2, 3, 3, 4, 2, 6, 4, 3, 1, 3, 3, 2, 3, 5, 3, 6, 2, 4, 3, 4, 4, 6, 4, 4, 2, 5, 3, 4, 3, 6, 4, 4, 2, 6, 6, 7, 4, 5, 3, 6, 1, 2, 3, 4, 3, 2, 2, 4, 3, 5, 5, 4, 3, 4, 6, 6, 2, 5, 4, 6, 3, 3, 4, 6, 4, 5, 6, 4, 4, 7, 4, 5, 2, 4, 5, 6, 3, 6, 4, 6, 3, 7, 6, 8, 4, 5, 4, 5, 2, 6, 6, 3, 6, 7, 7, 5, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 sequences computed from indices in prime factorization

FORMULA

a(n) = A000120(A005940(1+n)).

a(2n+1) = a(n).

A000035(a(n)) = A295895(n).

EXAMPLE

The first six levels of the binary tree (compare also to the illustration given at A005940):

                               1

                               |

                               1

                ............../ \..............

               2                               1

        ....../ \......                 ....../ \......

       2               2               2               1

      / \             / \             / \             / \

     /   \           /   \           /   \           /   \

    3     2         4     2         3     2         4     1

   / \   / \       / \   / \       / \   / \       / \   / \

  3   3 3   2     3   4 4   2     3   3 4   2     6   4 3   1

For n=0, the corresponding node in A005940(0+1) is 1, in binary also 1, thus a(0) = A000120(1) = 1.

For n=1, the corresponding node in A005940(1+1) is 2, in binary "10", thus a(1) = A000120(2) = 1.

For n=2, the corresponding node in A005940(1+2) is 3, in binary "11", thus a(2) = A000120(3) = 2.

For n=3, the corresponding node in A005940(1+3) is 4, in binary "100", thus a(3) = A000120(4) = 1.

PROG

(Scheme) (define (A295894 n) (A000120 (A005940 (+ 1 n))))

CROSSREFS

Cf. A000120, A003961, A005940, A295891, A295893, A295895.

Cf. A000225 (the positions of ones).

Sequence in context: A001227 A060764 A105149 * A068307 A158946 A223853

Adjacent sequences:  A295891 A295892 A295893 * A295895 A295896 A295897

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 30 2017

STATUS

approved

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Last modified February 21 00:32 EST 2018. Contains 299388 sequences. (Running on oeis4.)