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%I #11 Mar 03 2016 22:51:22
%S 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 30,35,20,27,14,11,64,93,90,109,84,123,98,85,72,105,102,125,76,111,62,
%U 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 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 Permutation of natural numbers obtained from the Ludic sieve. Note the indexing: Domain starts from 0, range from 1.
%C 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 1
%C |
%C ...................2...................
%C 4 3
%C 8......../ \........9 6......../ \........5
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 16 21 18 19 12 15 10 7
%C 32 45 42 49 36 51 38 31 24 33 30 35 20 27 14 11
%C etc.
%C Sequence A269387 is obtained from the mirror image of the same tree.
%H Antti Karttunen, <a href="/A269385/b269385.txt">Table of n, a(n) for n = 0..8191</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; after which, a(2n) = 2*a(n), a(2n+1) = A269379(a(n)).
%F As a composition of related permutations:
%F a(n) = A269171(A252755(n)).
%F a(n) = A260741(A269375(n)).
%F Other identities. For all n >= 2:
%F A000035(a(n)) = A000035(n). [This permutation preserves the parity of n from a(2)=4 onward.]
%o (Scheme, with memoization-macro definec)
%o (definec (A269385 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A269385 (/ n 2)))) (else (A269379 (A269385 (/ (- n 1) 2))))))
%Y Inverse: A269386.
%Y Cf. A000035, A269379.
%Y Cf. A003309 (right edge of the tree).
%Y Related or similar permutations: A163511, A260741, A269387, A269171.
%Y Cf. also A252755, A269375.
%K nonn,tabf
%O 0,2
%A _Antti Karttunen_, Mar 01 2016
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