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A330081 If the binary expansion of n is (b(1), ..., b(w)), then the binary expansion of a(n) is (b(1), b(3), b(5), ..., b(6), b(4), b(2)).

%I A330081 #16 Dec 10 2019 00:20:52
%S A330081 0,1,2,3,4,6,5,7,8,10,12,14,9,11,13,15,16,20,18,22,24,28,26,30,17,21,
%T A330081 19,23,25,29,27,31,32,36,40,44,34,38,42,46,48,52,56,60,50,54,58,62,33,
%U A330081 37,41,45,35,39,43,47,49,53,57,61,51,55,59,63,64,72,68,76
%N A330081 If the binary expansion of n is (b(1), ..., b(w)), then the binary expansion of a(n) is (b(1), b(3), b(5), ..., b(6), b(4), b(2)).
%C A330081 This sequence is a permutation of the nonnegative integers that preserves the binary length as well as the Hamming weight. See A330090 for the inverse.
%H A330081 Rémy Sigrist, <a href="/A330081/b330081.txt">Table of n, a(n) for n = 0..8192</a>
%H A330081 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A330081 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A330081 If n has w binary digits, then a^A003558(w-1)(n) = n (where a^k denotes the k-th iterate of the sequence).
%e A330081 For n = 1234:
%e A330081 - the binary expansion of 1234 is "10011010010",
%e A330081 - odd-indexed bits are "101100",
%e A330081 - even-indexed bits are "01001", and in reverse order "10010",
%e A330081 - hence the binary expansion of a(1234) is "10110010010",
%e A330081 - so a(1234) = 1426.
%o A330081 (PARI) shuffle(v) = { my (w=vector(#v), o=0, e=#v+1); for (k=1, #v, w[if (k%2, o++, e--)]=v[k]); w }
%o A330081 a(n) = fromdigits(shuffle(binary(n)), 2)
%Y A330081 See A329303 for a similar sequence.
%Y A330081 Cf. A003558, A194959, A330090 (inverse).
%K A330081 nonn,base,easy
%O A330081 0,3
%A A330081 _Rémy Sigrist_, Dec 01 2019