A295894 Binary weight of the contents of node n in Doudna-tree (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, 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

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: A060764 A105149 A355748 * A068307 A363721 A158946

Adjacent sequences: A295891 A295892 A295893 * A295895 A295896 A295897

Keyword

nonn

Author

Antti Karttunen, Nov 30 2017

Status

approved