cp's OEIS Frontend

A178729 a(n) = n XOR 3n, where XOR is bitwise XOR.

%I A178729 #35 Jun 21 2025 14:37:58
%S A178729 0,2,4,10,8,10,20,18,16,18,20,42,40,42,36,34,32,34,36,42,40,42,84,82,
%T A178729 80,82,84,74,72,74,68,66,64,66,68,74,72,74,84,82,80,82,84,170,168,170,
%U A178729 164,162,160,162,164,170,168,170,148,146,144,146,148,138,136,138,132,130
%N A178729 a(n) = n XOR 3n, where XOR is bitwise XOR.
%H A178729 Vincenzo Librandi, <a href="/A178729/b178729.txt">Table of n, a(n) for n = 0..5000</a>
%H A178729 Helena A. Verrill, <a href="https://arxiv.org/abs/2506.09509">Note on the negative base xor sequence n⊕-b(-n)</a>, arXiv:2506.09509 [math.NT], 2025.
%F A178729 a(n) = A005351(n) XOR A005352(n) (conjectured). Proved by Verrill link.
%F A178729 a(n) = 2 * A184617(n). - _Alois P. Heinz_, Jul 21 2017
%t A178729 f[n_] := BitXor[n, 3 n]; Array[f, 70, 0] (* _Robert G. Wilson v_, Jun 09 2010 *)
%o A178729 (PARI) a(n) = bitxor(n, 3*n); \\ _Michel Marcus_, Jul 11 2017
%o A178729 (Magma) [BitwiseXor(n, 3*n): n in [0..80]]; // _Vincenzo Librandi_, Jul 11 2017
%o A178729 (Python)
%o A178729 def A178729(n): return n^ 3*n # _Chai Wah Wu_, Jun 29 2022
%Y A178729 Cf. A048724, A048725, A178731, A178732, A178733, A178734, A178735, A178736. - _Robert G. Wilson v_, Jun 09 2010
%Y A178729 Cf. A184617.
%K A178729 nonn,look
%O A178729 0,2
%A A178729 _Dmitry Kamenetsky_, Jun 08 2010
%E A178729 a(30) onwards from _Robert G. Wilson v_, Jun 09 2010