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A269387 Tree of Ludic sieve: a(0) = 1, a(1) = 2; after which, a(2n) = A269379(a(n)), a(2n+1) = 2*a(n).

%I A269387 #10 Mar 03 2016 22:51:38
%S A269387 1,2,3,4,5,6,9,8,7,10,15,12,19,18,21,16,11,14,27,20,35,30,33,24,31,38,
%T A269387 51,36,49,42,45,32,13,22,39,28,65,54,57,40,59,70,87,60,79,66,69,48,55,
%U A269387 62,111,76,125,102,105,72,85,98,123,84,109,90,93,64,17,26,63,44,95,78,81,56,113,130,159,108,139,114,117,80
%N A269387 Tree of Ludic sieve: a(0) = 1, a(1) = 2; after which, a(2n) = A269379(a(n)), a(2n+1) = 2*a(n).
%C A269387 Permutation of natural numbers obtained from the Ludic sieve. Note the indexing: Domain starts from 0, range from 1.
%C A269387 This sequence can be represented as a binary tree. Each left hand child is obtained by applying A269379 to the parent's contents, and each right hand child is obtained by doubling the parent's contents:
%C A269387                                     1
%C A269387                                     |
%C A269387                  ...................2...................
%C A269387                 3                                       4
%C A269387       5......../ \........6                   9......../ \........8
%C A269387      / \                 / \                 / \                 / \
%C A269387     /   \               /   \               /   \               /   \
%C A269387    /     \             /     \             /     \             /     \
%C A269387   7       10         15       12         19       18         21       16
%C A269387 11 14   27  20     35  30   33  24     31  38   51  36     49  42   45  32
%C A269387 etc.
%C A269387 Sequence A269385 is obtained from the mirror image of the same tree.
%H A269387 Antti Karttunen, <a href="/A269387/b269387.txt">Table of n, a(n) for n = 0..8191</a>
%H A269387 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269387 a(0) = 1, a(1) = 2; after which, a(2n) = A269379(a(n)), a(2n+1) = 2*a(n).
%F A269387 As a composition of other permutations:
%F A269387 a(n) = A269171(A252753(n)).
%F A269387 a(n) = A260741(A269377(n)).
%o A269387 (Scheme, with memoization-macro definec)
%o A269387 (definec (A269387 n) (cond ((<= n 2) (+ 1 n)) ((even? n) (A269379 (A269387 (/ n 2)))) (else (* 2 (A269387 (/ (- n 1) 2))))))
%Y A269387 Inverse: A269388.
%Y A269387 Cf. A003309 (left edge of the tree).
%Y A269387 Cf. A269379.
%Y A269387 Related permutations: A260741, A269171, A269385.
%Y A269387 Cf. also A252753, A269377.
%K A269387 nonn,tabf
%O A269387 0,2
%A A269387 _Antti Karttunen_, Mar 01 2016