%I
%S 1,2,4,3,8,5,6,7,16,17,10,19,12,11,14,9,32,41,34,61,20,23,38,27,24,29,
%T 22,39,28,35,18,13,64,89,82,145,68,95,122,91,40,53,46,81,76,107,54,45,
%U 48,65,58,103,44,59,78,57,56,77,70,123,36,47,26,15,128,185,178,313,164,239,290,217,136,197,190,333,244,359,182,147,80
%N Tree of Lucky sieve, mirrored: a(0) = 1, a(1) = 2; after which a(2n) = 2*a(n), a(2n+1) = A269369(a(n)).
%C Permutation of natural numbers obtained from the Lucky 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 A269369 to the parent's contents:
%C 1
%C 
%C ...................2...................
%C 4 3
%C 8......../ \........5 6......../ \........7
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C / \ / \ / \ / \
%C 16 17 10 19 12 11 14 9
%C 32 41 34 61 20 23 38 27 24 29 22 39 28 35 18 13
%C etc.
%C Sequence A269377 is obtained from the mirror image of the same tree.
%H Antti Karttunen, <a href="/A269375/b269375.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; after which, a(2n) = 2*a(n), a(2n+1) = A269369(a(n)).
%F As a composition of related permutations:
%F a(n) = A260742(A269385(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 memoizationmacro definec)
%o (definec (A269375 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A269375 (/ n 2)))) (else (A269369 (A269375 (/ ( n 1) 2))))))
%Y Inverse: A269376.
%Y Cf. A000035, A269369.
%Y Cf. A000959 (with 2 inserted between 1 and 3 forms the right edge of the tree).
%Y Related or similar permutations: A163511, A260742, A269377.
%Y Cf. also A252755, A269385.
%K nonn,tabf
%O 0,2
%A _Antti Karttunen_, Mar 01 2016
