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%I #19 Sep 09 2017 19:24:38
%S 0,1,1,2,2,3,3,4,4,5,6,5,7,6,7,8,8,9,10,11,9,12,13,10,14,11,12,15,13,
%T 14,15,16,16,17,18,19,20,17,21,22,23,18,24,25,19,26,20,21,27,28,22,29,
%U 23,24,30,25,26,27,31,28,29,30,31,32,32,33,34,35,36,37,33,38,39,40,41,34,42,43,44,35,45,46,36,47
%N If A051135(n) = 1, then a(n) = A004001(n) - 1, otherwise a(n) = n - A004001(n).
%C For n > 1, a(n) gives the contents of the parent of the node which contains n in A267112-tree.
%C Each n > 0 occurs exactly twice, in positions A088359(n) and A087686(n+1).
%C The sequence maps each n > 1 to a number which is one digit shorter in binary system (cf. "Other identities"). This follows because A004001 is monotonic and A004001(2^n) = 2^(n-1) (see properties (2) and (3) given on page 227 of Kubo & Vakil paper, or page 3 in PDF), and also how the frequency counts Q_n for A004001 are recursively constructed (see Kubo & Vakil paper, p. 229 or A265332 for the illustration).
%H Antti Karttunen, <a href="/A267110/b267110.txt">Table of n, a(n) for n = 1..8192</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.
%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F If A051135(n) = 1 [Equally: if A265332(n) = 1], then a(n) = A004001(n) - 1, otherwise a(n) = n - A004001(n).
%F Other identities. For all n >= 2:
%F A070939(a(n)) = A070939(n) - 1. [See Comments section.]
%o (Scheme) (define (A267110 n) (if (= 1 (A051135 n)) (- (A004001 n) 1) (- n (A004001 n))))
%Y Cf. A004001, A051135, A070939, A087686, A088359, A265332, A267108, A267109, A267112.
%K nonn,look
%O 1,4
%A _Antti Karttunen_, Jan 16 2016
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