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A283977 a(2n) = A002487(n), a(2n+1) = A002487(n) XOR A002487(n+1), where XOR is bitwise-xor (A003987).

%I A283977 #11 Mar 23 2017 11:44:04
%S A283977 0,1,1,0,1,3,2,3,1,2,3,1,2,1,3,2,1,5,4,7,3,6,5,7,2,7,5,6,3,7,4,5,1,4,
%T A283977 5,1,4,3,7,4,3,11,8,13,5,2,7,5,2,5,7,2,5,13,8,11,3,4,7,3,4,1,5,4,1,7,
%U A283977 6,3,5,12,9,13,4,15,11,12,7,13,10,9,3,8,11,3,8,5,13,8,5,9,12,11,7,14,9,11,2,11,9,14,7,11,12,9,5,8,13,5,8,3,11,8,3
%N A283977 a(2n) = A002487(n), a(2n+1) = A002487(n) XOR A002487(n+1), where XOR is bitwise-xor (A003987).
%H A283977 Antti Karttunen, <a href="/A283977/b283977.txt">Table of n, a(n) for n = 0..8192</a>
%H A283977 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A283977 a(2n) = A002487(2n) = A002487(n), a(2n+1) = A002487(n) XOR A002487(n+1), where XOR is bitwise-xor (A003987).
%F A283977 a(n) = A283976(n) - A283978(n).
%F A283977 a(n) = A002487(n) - 2*A283978(n).
%t A283977 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ@ n, a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[If[EvenQ@ n, a[n/2], BitXor[a[#], a[# + 1]] &[(n - 1)/2]], {n, 0, 112}] (* _Michael De Vlieger_, Mar 22 2017 *)
%o A283977 (Scheme) (define (A283977 n) (if (even? n) (A002487 n) (A003987bi (A002487 (/ (- n 1) 2)) (A002487 (/ (+ n 1) 2))))) ;; Where A003987bi implements bitwise-XOR (A003987).
%o A283977 (PARI) A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
%o A283977 a(n) = if(n<2, n, if(n%2, bitxor(A(n\2), A((n + 1)/2)), A(n\2)));
%o A283977 for(n=0, 120, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 23 2017
%Y A283977 Bisections: A002487, A283987.
%Y A283977 Cf. A003987, A283976, A283978.
%K A283977 nonn,base
%O A283977 0,6
%A A283977 _Antti Karttunen_, Mar 21 2017