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A269171 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269379(a(A268674(2n+1))).

%I A269171 #16 Mar 03 2016 22:48:23
%S A269171 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,23,20,21,22,25,24,19,26,
%T A269171 27,28,29,30,37,32,33,34,35,36,41,46,39,40,43,42,47,44,45,50,53,48,31,
%U A269171 38,51,52,61,54,49,56,57,58,67,60,71,74,63,64,65,66,77,68,69,70,83,72,89,82,75,92,59,78,91,80,81,86,97,84,79,94,87,88,107,90,85,100
%N A269171 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269379(a(A268674(2n+1))).
%H A269171 Antti Karttunen, <a href="/A269171/b269171.txt">Table of n, a(n) for n = 1..8192</a>
%H A269171 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269171 a(1) = 1, then after for even n, a(n) = 2*a(n/2), and for odd n, a(n) = A269379(a(A268674(n))).
%F A269171 a(1) = 1, for n > 1, a(n) = A255127(A055396(n), a(A078898(n))).
%F A269171 As a composition of other permutations:
%F A269171 a(n) = A269385(A252756(n)).
%F A269171 a(n) = A269387(A252754(n)).
%F A269171 Other identities. For all n >= 1:
%F A269171 A000035(a(n)) = A000035(n). [Preserves the parity of n.]
%F A269171 a(A008578(n)) = A003309(n). [Maps noncomposites to Ludic numbers.]
%o A269171 (Scheme, two versions, both using memoization-macro definec)
%o A269171 (definec (A269171 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269171 (/ n 2)))) (else (A269379 (A269171 (A268674 n))))))
%o A269171 (definec (A269171 n) (if (<= n 1) n (A255127bi (A055396 n) (A269171 (A078898 n))))) ;; Code for A255127bi given in A255127.
%Y A269171 Inverse: A269172.
%Y A269171 Cf. A000035, A003309, A008578, A055396, A078898, A268674, A255127, A269379.
%Y A269171 Related or similar permutations: A260741, A260742, A269355, A269357, A255421, A252754, A252756, A269385, A269387.
%Y A269171 Cf. also A269393 (a(3n)/3) and A269395.
%Y A269171 Differs from A255407 for the first time at n=38, where a(38) = 46, while A255407(38) = 38.
%K A269171 nonn
%O A269171 1,2
%A A269171 _Antti Karttunen_, Mar 03 2016