A330081 - OEIS

%I #16 Dec 10 2019 00:20:52

%S 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 19,23,25,29,27,31,32,36,40,44,34,38,42,46,48,52,56,60,50,54,58,62,33,

%U 37,41,45,35,39,43,47,49,53,57,61,51,55,59,63,64,72,68,76

%N 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 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 Rémy Sigrist, <a href="/A330081/b330081.txt">Table of n, a(n) for n = 0..8192</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F 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 For n = 1234:

%e - the binary expansion of 1234 is "10011010010",

%e - odd-indexed bits are "101100",

%e - even-indexed bits are "01001", and in reverse order "10010",

%e - hence the binary expansion of a(1234) is "10110010010",

%e - so a(1234) = 1426.

%o (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 a(n) = fromdigits(shuffle(binary(n)), 2)

%Y See A329303 for a similar sequence.

%Y Cf. A003558, A194959, A330090 (inverse).

%K nonn,base,easy

%O 0,3

%A _Rémy Sigrist_, Dec 01 2019