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A269385 Tree of Ludic sieve, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)).

%I A269385 #11 Mar 03 2016 22:51:22
%S A269385 1,2,4,3,8,9,6,5,16,21,18,19,12,15,10,7,32,45,42,49,36,51,38,31,24,33,
%T A269385 30,35,20,27,14,11,64,93,90,109,84,123,98,85,72,105,102,125,76,111,62,
%U A269385 55,48,69,66,79,60,87,70,59,40,57,54,65,28,39,22,13,128,189,186,229,180,267,218,191,168,249,246,305,196,291,170,151,144
%N A269385 Tree of Ludic sieve, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)).
%C A269385 Permutation of natural numbers obtained from the Ludic sieve. Note the indexing: Domain starts from 0, range from 1.
%C A269385 This sequence can be represented as a binary tree. Each left hand child is obtained by doubling the parent's contents, and each right hand child is obtained by applying A269379 to the parent's contents:
%C A269385                                      1
%C A269385                                      |
%C A269385                   ...................2...................
%C A269385                  4                                       3
%C A269385        8......../ \........9                   6......../ \........5
%C A269385       / \                 / \                 / \                 / \
%C A269385      /   \               /   \               /   \               /   \
%C A269385     /     \             /     \             /     \             /     \
%C A269385   16       21         18       19         12       15         10       7
%C A269385 32  45   42  49     36  51   38  31     24  33   30  35     20  27   14 11
%C A269385 etc.
%C A269385 Sequence A269387 is obtained from the mirror image of the same tree.
%H A269385 Antti Karttunen, <a href="/A269385/b269385.txt">Table of n, a(n) for n = 0..8191</a>
%H A269385 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269385 a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)).
%F A269385 As a composition of related permutations:
%F A269385 a(n) = A269171(A252755(n)).
%F A269385 a(n) = A260741(A269375(n)).
%F A269385 Other identities. For all n >= 2:
%F A269385 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n from a(2)=4 onward.]
%o A269385 (Scheme, with memoization-macro definec)
%o A269385 (definec (A269385 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A269385 (/ n 2)))) (else (A269379 (A269385 (/ (- n 1) 2))))))
%Y A269385 Inverse: A269386.
%Y A269385 Cf. A000035, A269379.
%Y A269385 Cf. A003309 (right edge of the tree).
%Y A269385 Related or similar permutations: A163511, A260741, A269387, A269171.
%Y A269385 Cf. also A252755, A269375.
%K A269385 nonn,tabf
%O A269385 0,2
%A A269385 _Antti Karttunen_, Mar 01 2016