A266640 - OEIS

%I #13 Jan 29 2016 17:13:51

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A266640/b266640.txt">Table of n, a(n) for n = 1..8191</a>

%H T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252.

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

%F Other identities. For all n >= 0:

%F a(2^n) = n+1.

%e Illustration how the sequence can be constructed by concatenating the reversed reduced frequency counts R_n of each successive level n of A004001-tree:

%e                               1

%e                              / \

%e                             2   1

%e                            /|\   \

%e               ____________3 2 1   1

%e              /    /    /  | |\ \   \

%e     ________4  __3    2   1 2 1 1   1

%e    / / / / /  / /|   /|   | |\ \ \   \

%e   5 4 3 2 1  3 2 1  2 1   1 2 1 1 1   1

%e etc.

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

%Y Cf. A004001, A054429.

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

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

%K nonn,tabf

%O 1,2

%A _Antti Karttunen_, Jan 22 2016