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A275716 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).

%I A275716 #7 Aug 07 2016 20:44:23
%S A275716 1,2,9,3,42,17,12,4,209,115,82,41,59,26,19,5,1042,801,572,444,409,283,
%T A275716 202,57,292,180,129,48,92,31,22,6,5209,5603,4002,4881,2859,3106,2219,
%U A275716 733,2042,1977,1412,620,1009,395,282,97,1459,1258,899,525,642,334,239,74,459,213,152,63,109,40,29,7,26042,39217
%N A275716 Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).
%C A275716 Note the indexing: the domain starts from 0, while the range excludes zero.
%C A275716 This sequence can be represented as a binary tree. Each left hand child is obtained by applying A273669(n) when the parent contains n, and each right hand child is obtained by applying A273664 to the parent's contents:
%C A275716                                      1
%C A275716                                      |
%C A275716                   ...................2...................
%C A275716                  9                                       3
%C A275716       42......../ \........17                 12......../ \........4
%C A275716       / \                 / \                 / \                 / \
%C A275716      /   \               /   \               /   \               /   \
%C A275716     /     \             /     \             /     \             /     \
%C A275716   209     115         82       41         59       26         19       5
%C A275716 1042 801 572 444   409  283 202  57    292  180  129 48     92  31   22 6
%C A275716 etc.
%H A275716 Antti Karttunen, <a href="/A275716/b275716.txt">Table of n, a(n) for n = 0..4095</a>
%H A275716 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A275716 a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).
%F A275716 As a composition of other permutations:
%F A275716 a(n) = A249824(A163511(n)).
%o A275716 (Scheme, with memoization-macro definec)
%o A275716 (definec (A275716 n) (cond ((<= n 1) (+ 1 n)) ((even? n) (A273669 (A275716 (/ n 2)))) (else (A273664 (A275716 (/ (- n 1) 2))))))
%Y A275716 Inverse: A275715.
%Y A275716 Cf. A273664, A273669.
%Y A275716 Related or similar permutations: A163511, A249824, A245612.
%K A275716 nonn,tabf
%O A275716 0,2
%A A275716 _Antti Karttunen_, Aug 06 2016