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%I #12 Jun 07 2014 01:36:24
%S 1,4,2,12,6,8,3,32,19,18,10,24,13,9,5,84,53,50,31,49,30,27,15,63,38,
%T 36,21,25,14,16,7,220,138,136,86,128,82,81,51,126,79,80,47,72,42,44,
%U 23,162,103,99,62,96,59,54,34,64,39,40,22,45,26,20,11,564,365
%N a(1) = 1, a(2n) = A013929(a(n)), a(2n+1) = A005117(1+a(n)).
%C This permutation entangles complementary pair odd/even numbers (A005408/A005843) with complementary pair A005117/A013929 (numbers which are squarefree/not squarefree).
%H Antti Karttunen, <a href="/A243344/b243344.txt">Table of n, a(n) for n = 1..4095</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, a(2n) = A013929(a(n)), a(2n+1) = A005117(1+a(n)).
%F For all n, A008966(a(n)) = A000035(n), or equally, mu(a(n)) = n modulo 2, where mu is Moebius mu (A008683). [The same property holds for A088610.]
%o (Scheme, with memoizing definec-macro from _Antti Karttunen_'s IntSeq-library)
%o (definec (A243344 n) (cond ((<= n 1) n) ((even? n) (A013929 (A243344 (/ n 2)))) (else (A005117 (+ 1 (A243344 (/ (- n 1) 2)))))))
%Y Inverse: A243343.
%Y Cf. A005843, A005408, A008966, A005117, A013929, A013928, A057627.
%Y Similar permutations: A088610 (simple variant), A243345-A243346, A243347, A243287-A243288, A135141-A227413, A237126-A237427, A193231.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 03 2014
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