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A255567 a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).

%I A255567 #25 May 30 2016 18:23:09
%S A255567 1,2,3,12,13,16,17,72,73,76,77,90,91,94,95,480,481,484,485,498,499,
%T A255567 502,503,576,577,580,581,594,595,598,599,3600,3601,3604,3605,3618,
%U A255567 3619,3622,3623,3696,3697,3700,3701,3714,3715,3718,3719,4200,4201,4204,4205,4218,4219,4222,4223,4296,4297,4300,4301,4314,4315,4318,4319
%N A255567 a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).
%C A255567 From 2 onward, the sequence seems to give those n for which A256450(A255411(n))+1 = A255411(A256450(n)), i.e., grandparents for those cousins in tree A255566 where the cousin at the right side is one more than the cousin at the left side.
%H A255567 Antti Karttunen, <a href="/A255567/b255567.txt">Table of n, a(n) for n = 1..1023</a>
%F A255567 a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).
%e A255567 This sequence can be represented as a binary tree. Apart from the 1 at root, and its children 2 and 3, from then on each left hand child is produced as A255411(n), and each right hand child as 1 + A255411(n) when parent contains n >= 2:
%e A255567                    ..................1..................
%e A255567                   2                                     3
%e A255567         12......./ \.......13                 16......./ \.......17
%e A255567        / \                 / \               / \                 / \
%e A255567       /   \               /   \             /   \               /   \
%e A255567      /     \             /     \           /     \             /     \
%e A255567    72       73         76       77       90       91         94       95
%e A255567 480  481 484  485   498  499 502  503 576  577 580  581   594  595 598  599
%e A255567 etc.
%o A255567 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A255567 (definec (A255567 n) (cond ((<= n 2) n) ((odd? n) (+ 1 (A255567 (- n 1)))) (else (A255411 (A255567 (/ n 2))))))
%o A255567 ;; This for now conjectured to be equal from a(2) onward:
%o A255567 (define A255567 (MATCHING-POS 2 1 (lambda (n) (= (+ 1 (A256450 (A255411 n))) (A255411 (A256450 n))))))
%Y A255567 Cf. A256450, A255411. See also the tree illustration in A255566.
%K A255567 nonn
%O A255567 1,2
%A A255567 _Antti Karttunen_, May 05 2015
%E A255567 Edited because of the changed starting offset of A256450 - _Antti Karttunen_, May 30 2016