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%I #7 Mar 03 2016 22:51:45
%S 0,1,2,3,4,5,8,7,6,9,16,11,32,17,10,15,64,13,12,19,14,33,128,23,256,
%T 65,18,35,512,21,24,31,22,129,20,27,1024,25,34,39,2048,29,4096,67,30,
%U 257,8192,47,28,513,26,131,16384,37,48,71,38,1025,40,43,32768,49,66,63,36,45,65536,259,46,41,131072,55,96,2049,130,51,262144,69,44
%N Permutation of natural numbers: a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A269380(n)).
%C Note the indexing: Domain starts from 1, range from 0.
%H Antti Karttunen, <a href="/A269388/b269388.txt">Table of n, a(n) for n = 1..1024</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A269380(n)).
%F As a composition of other permutations:
%F a(n) = A252754(A269172(n)).
%F a(n) = A269378(A260742(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A269388 n) (cond ((= 1 n) (- n 1)) ((even? n) (+ 1 (* 2 (A269388 (/ n 2))))) (else (* 2 (A269388 (A269380 n))))))
%Y Inverse: A269387.
%Y Cf. A269380.
%Y Related permutations: A260742, A269386, A269172.
%Y Cf. also A252754, A269378.
%Y Differs from A156552, A252754 and A246677(n-1) for the first time at n=19, which here a(19)=12, instead of 128.
%K nonn
%O 1,3
%A _Antti Karttunen_, Mar 01 2016