A266640 Reversed reduced frequency counts for A004001: a(n) = A265754(A054429(n)).

1, 2, 1, 3, 2, 1, 1, 4, 3, 2, 1, 2, 1, 1, 1, 5, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 6, 5, 4, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 7, 6, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 4, 3, 2, 1, 3, 2, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 1

Offset

1,2

Comments

Deleting all 1's and decrementing the remaining terms by one gives the sequence back.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.

Formula

a(n) = A265754(A054429(n)).

Other identities. For all n >= 0:

a(2^n) = n+1.

Example

Illustration how the sequence can be constructed by concatenating the reversed reduced frequency counts R_n of each successive level n of A004001-tree:
                              1
                             / \
                            2   1
                           /|\   \
              ____________3 2 1   1
             /    /    /  | |\ \   \
    ________4  __3    2   1 2 1 1   1
   / / / / /  / /|   /|   | |\ \ \   \
  5 4 3 2 1  3 2 1  2 1   1 2 1 1 1   1
etc.

Prog

(Scheme) (define (A266640 n) (A265754 (A054429 n)))

Crossrefs

Cf. A004001, A054429.

Cf. A000079 (positions of records, where n appears for the first time).

Cf. A265754 (obtained from the mirror image of the same tree).

Sequence in context: A366281 A365805 A334749 * A359350 A065120 A176206

Adjacent sequences: A266637 A266638 A266639 * A266641 A266642 A266643

Keyword

nonn,tabf

Author

Antti Karttunen, Jan 22 2016

Status

approved