%I #7 Aug 07 2016 20:44:23

%S 1,2,9,3,42,17,12,4,209,115,82,41,59,26,19,5,1042,801,572,444,409,283,

%T 202,57,292,180,129,48,92,31,22,6,5209,5603,4002,4881,2859,3106,2219,

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

%C Note the indexing: the domain starts from 0, while the range excludes zero.

%C 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 1

%C |

%C ...................2...................

%C 9 3

%C 42......../ \........17 12......../ \........4

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C / \ / \ / \ / \

%C 209 115 82 41 59 26 19 5

%C 1042 801 572 444 409 283 202 57 292 180 129 48 92 31 22 6

%C etc.

%H Antti Karttunen, <a href="/A275716/b275716.txt">Table of n, a(n) for n = 0..4095</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).

%F As a composition of other permutations:

%F a(n) = A249824(A163511(n)).

%o (Scheme, with memoization-macro definec)

%o (definec (A275716 n) (cond ((<= n 1) (+ 1 n)) ((even? n) (A273669 (A275716 (/ n 2)))) (else (A273664 (A275716 (/ (- n 1) 2))))))

%Y Inverse: A275715.

%Y Cf. A273664, A273669.

%Y Related or similar permutations: A163511, A249824, A245612.

%K nonn,tabf

%O 0,2

%A _Antti Karttunen_, Aug 06 2016