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A269172 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A269380(2n+1))).

%I A269172 #16 Mar 03 2016 22:48:29
%S A269172 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,25,20,21,22,19,24,23,26,
%T A269172 27,28,29,30,49,32,33,34,35,36,31,50,39,40,37,42,41,44,45,38,43,48,55,
%U A269172 46,51,52,47,54,121,56,57,58,77,60,53,98,63,64,65,66,59,68,69,70,61,72,169,62,75,100,67,78,85,80,81
%N A269172 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A269380(2n+1))).
%H A269172 Antti Karttunen, <a href="/A269172/b269172.txt">Table of n, a(n) for n = 1..2244</a>
%H A269172 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269172 a(1) = 1, then after for even n, a(n) = 2*a(n/2), and for odd n, A250469(a(A269380(n))).
%F A269172 a(1) = 1, for n > 1, a(n) = A083221(A260738(n), a(A260739(n))).
%F A269172 As a composition of other permutations:
%F A269172 a(n) = A252755(A269386(n)).
%F A269172 a(n) = A252753(A269388(n)).
%F A269172 Other identities. For all n >= 1:
%F A269172 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%F A269172 a(A003309(n)) = A008578(n). [Maps Ludic numbers to noncomposites.]
%o A269172 (Scheme, two versions, both using memoization-macro definec)
%o A269172 (definec (A269172 n) (cond ((<= n 1) n) ((even? n) (* 2 (A269172 (/ n 2)))) (else (A250469 (A269172 (A269380 n))))))
%o A269172 (definec (A269172 n) (if (<= n 1) n (A083221bi (A260738 n) (A269172 (A260739 n))))) ;; Code for A083221bi given in A083221.
%Y A269172 Inverse: A269171.
%Y A269172 Cf. A000035, A003309, A008578, A083221, A250469, A260738, A260739, A269380.
%Y A269172 Related or similar permutations: A260741, A260742, A269356, A269358, A255422.
%Y A269172 Cf. also A269394 (a(3n)/3) and A269396.
%Y A269172 Differs from A255408 for the first time at n=38, where a(38) = 50, while A255408(38) = 38.
%K A269172 nonn
%O A269172 1,2
%A A269172 _Antti Karttunen_, Mar 03 2016