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%I #13 Dec 26 2019 15:43:46
%S 0,1,2,3,4,6,8,12,7,16,5,24,14,32,10,48,28,64,20,13,96,15,9,56,128,40,
%T 26,192,30,18,112,256,80,52,384,60,36,11,224,512,25,160,29,17,104,768,
%U 120,72,22,448,1024,50,320,31,58,34,208,1536,240,144,44,896,2048,100,640,62,116,68,21,416,3072,27,49,480,288,88,57
%N a(1) = 0; a(2) = 1; and for n > 2, a(n) = A330682(n) + 2*a(A329904(n)).
%C Note the indexing: domain begins from one, but the range contains also zero.
%H Antti Karttunen, <a href="/A329905/b329905.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 0; a(2) = 1; and for n > 2, if A181815(n) is odd, a(n) = 1 + 2*a(A329904(n)), otherwise a(n) = 2*a(A329904(n)).
%F a(n) = A243071(A181815(n)).
%F For all n >= 1, A000120(a(n)) = A061394(n).
%F For all n >= 2, A070939(a(n)) = A329907(n).
%o (PARI) A329905(n) = if(n<=2,n-1,(A181815(n)%2)+2*(A329905(A329904(n))));
%Y Cf. A329906 (inverse permutation).
%Y Cf. A000035, A025487, A061394, A181815, A243071, A329897, A329898, A329904, A329907, A330682.
%K nonn
%O 1,3
%A _Antti Karttunen_, Dec 24 2019
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