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A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.

%I A269374 #9 Mar 07 2016 12:12:15
%S A269374 1,2,3,6,5,4,11,8,9,10,7,18,21,28,15,12,17,22,19,38,13,16,35,26,41,58,
%T A269374 55,102,29,40,23,14,33,46,43,80,37,52,75,56,25,34,31,60,69,100,51,44,
%U A269374 81,118,115,206,109,160,203,152,57,82,79,144,45,64,27,20,65,94,91,164,85,124,159,120,73,106,103,186,149,220,111,96,49
%N A269374 Permutation of natural numbers: a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.
%C A269374 Permutation obtained from the Lucky sieve.
%C A269374 This sequence can be represented as a binary tree. For n > 2, each left hand child is obtained by doubling the contents of the parent node and subtracting one, and each right hand child is obtained by applying A269372(n), when the parent node contains n:
%C A269374                                     1
%C A269374                                     |
%C A269374                  ...................2...................
%C A269374                 3                                       6
%C A269374       5......../ \........4                  11......../ \........8
%C A269374      / \                 / \                 / \                 / \
%C A269374     /   \               /   \               /   \               /   \
%C A269374    /     \             /     \             /     \             /     \
%C A269374   9       10          7       18         21       28         15       12
%C A269374 17 22   19  38      13 16   35  26     41  58   55  102    29  40   23  14
%C A269374 etc.
%H A269374 Antti Karttunen, <a href="/A269374/b269374.txt">Table of n, a(n) for n = 1..4096</a>
%H A269374 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269374 a(1) = 1, a(n) = A255551(A001511(n), a(A003602(n))) - 1.
%F A269374 a(1) = 1, a(2n) = A269372(a(n)), a(2n+1) = (2*a(n+1))-1.
%F A269374 Other identities. For all n >= 0:
%F A269374 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%o A269374 (Scheme, two different implementations, both using memoization-macro definec)
%o A269374 (definec (A269374 n) (cond ((<= n 1) n) (else (+ -1 (A255551bi (A001511 n) (A269374 (A003602 n))))))) ;; Code for A255551bi given in A255551.
%o A269374 (definec (A269374 n) (cond ((<= n 1) n) ((even? n) (A269372 (A269374 (/ n 2)))) (else (+ -1 (* 2 (A269374 (/ (+ n 1) 2)))))))
%Y A269374 Inverse: A269373.
%Y A269374 Cf. A000035, A001511, A003602, A255551, A269372.
%Y A269374 Cf. also A269375, A269377 and also A249814, A269384.
%K A269374 nonn,tabf
%O A269374 1,2
%A A269374 _Antti Karttunen_, Mar 01 2016