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A243346 a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A013929(a(n)), where A005117 are squarefree and A013929 are nonsquarefree numbers.

%I A243346 #11 Jun 08 2014 08:58:57
%S A243346 1,2,4,3,8,6,12,5,9,13,24,10,18,19,32,7,16,14,25,21,36,38,63,15,27,30,
%T A243346 49,31,50,53,84,11,20,26,45,22,40,39,64,34,54,59,96,62,99,103,162,23,
%U A243346 44,42,72,47,80,79,126,51,81,82,128,86,136,138,220,17,28,33,52,41,68,73,120
%N A243346 a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A013929(a(n)), where A005117 are squarefree and A013929 are nonsquarefree numbers.
%C A243346 This permutation entangles complementary pair A005843/A005408 (even/odd numbers) with complementary pair A005117/A013929 (numbers which are squarefree/are not squarefree).
%H A243346 Antti Karttunen, <a href="/A243346/b243346.txt">Table of n, a(n) for n = 1..8189</a>
%H A243346 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A243346 a(1) = 1, a(2n) = A005117(1+a(n)), a(2n+1) = A013929(a(n)).
%F A243346 For all n > 1, A008966(a(n)) = A000035(n+1), or equally, mu(a(n)) + 1 = n modulo 2, where mu is Moebius mu (A008683). [A property shared with a simpler variant A075378].
%o A243346 (Scheme, with memoizing macro definec from _Antti Karttunen_'s IntSeq-library)
%o A243346 (definec (A243346 n) (cond ((<= n 1) n) ((even? n) (A005117 (+ 1 (A243346 (/ n 2))))) (else (A013929 (A243346 (/ (- n 1) 2))))))
%Y A243346 Inverse: A243345.
%Y A243346 Cf. A005843, A005408, A008966, A005117, A013929, A013928, A057627.
%Y A243346 Similar permutations: A075378, A243343-A243344, A243347, A243287-A243288, A135141-A227413, A237126-A237427, A193231.
%K A243346 nonn
%O A243346 1,2
%A A243346 _Antti Karttunen_, Jun 03 2014