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%I #25 May 30 2016 18:23:09
%S 1,2,3,12,13,16,17,72,73,76,77,90,91,94,95,480,481,484,485,498,499,
%T 502,503,576,577,580,581,594,595,598,599,3600,3601,3604,3605,3618,
%U 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 a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).
%C 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 Antti Karttunen, <a href="/A255567/b255567.txt">Table of n, a(n) for n = 1..1023</a>
%F a(1) = 1, a(2) = 2, after which, a(2n+1) = 1 + a(2n), a(2n) = A255411(a(n)).
%e 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 ..................1..................
%e 2 3
%e 12......./ \.......13 16......./ \.......17
%e / \ / \ / \ / \
%e / \ / \ / \ / \
%e / \ / \ / \ / \
%e 72 73 76 77 90 91 94 95
%e 480 481 484 485 498 499 502 503 576 577 580 581 594 595 598 599
%e etc.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (definec (A255567 n) (cond ((<= n 2) n) ((odd? n) (+ 1 (A255567 (- n 1)))) (else (A255411 (A255567 (/ n 2))))))
%o ;; This for now conjectured to be equal from a(2) onward:
%o (define A255567 (MATCHING-POS 2 1 (lambda (n) (= (+ 1 (A256450 (A255411 n))) (A255411 (A256450 n))))))
%Y Cf. A256450, A255411. See also the tree illustration in A255566.
%K nonn
%O 1,2
%A _Antti Karttunen_, May 05 2015
%E Edited because of the changed starting offset of A256450 - _Antti Karttunen_, May 30 2016
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