cp's OEIS Frontend

A375184 In the binary expansion of n, complement bits at even positions and to the right of a 0 (the most significant bit corresponding to position 1).

%I A375184 #9 Aug 06 2024 16:38:41
%S A375184 0,1,2,3,4,5,6,7,9,8,10,11,13,12,14,15,18,19,16,17,20,21,22,23,26,27,
%T A375184 24,25,28,29,30,31,37,36,38,39,33,32,34,35,41,40,42,43,45,44,46,47,53,
%U A375184 52,54,55,49,48,50,51,57,56,58,59,61,60,62,63,74,75,72,73
%N A375184 In the binary expansion of n, complement bits at even positions and to the right of a 0 (the most significant bit corresponding to position 1).
%C A375184 This sequence is a self-inverse permutation of the nonnegative integers.
%H A375184 Rémy Sigrist, <a href="/A375184/b375184.txt">Table of n, a(n) for n = 0..8191</a>
%H A375184 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A375184 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A375184 a(floor(n/2)) = floor(a(n)/2).
%e A375184 For n = 9: the binary expansion of 9 is "1001": the bit at position 2 (0) sits to the right of a 1 so we keep it, the bit at position 4 (1) sits to the right of a 0 so we complement it; the binary expansion of a(9) is "1000" and a(9) = 8.
%o A375184 (PARI) a(n) = { my (b = binary(n)); forstep (k = 2, #b, 2, if (!b[k-1], b[k] = 1-b[k];);); fromdigits(b, 2); }
%Y A375184 Cf. A063946, A165199, A375183.
%K A375184 nonn,base
%O A375184 0,3
%A A375184 _Rémy Sigrist_, Aug 03 2024