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A283978 a(2n) = 0, a(2n+1) = A002487(n) AND A002487(n+1), where AND is bitwise-and (A004198).

%I A283978 #11 Mar 23 2017 11:44:10
%S A283978 0,0,0,1,0,0,0,0,0,1,0,2,0,2,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,
%T A283978 0,4,0,4,0,3,0,0,0,0,0,5,0,2,0,2,0,5,0,0,0,0,0,3,0,4,0,4,0,1,0,0,0,4,
%U A283978 0,1,0,0,0,0,0,3,0,2,0,2,0,3,0,8,0,8,0,5,0,4,0,4,0,1,0,0,0,0,0,1,0,4,0,4,0,5,0,8,0,8,0,3,0,2,0,2,0,3,0,0,0
%N A283978 a(2n) = 0, a(2n+1) = A002487(n) AND A002487(n+1), where AND is bitwise-and (A004198).
%H A283978 Antti Karttunen, <a href="/A283978/b283978.txt">Table of n, a(n) for n = 0..8192</a>
%H A283978 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A283978 a(2n) = 0, a(2n+1) = A002487(n) AND A002487(n+1), where AND is bitwise-and (A004198).
%F A283978 a(n) = A283976(n) - A283977(n).
%F A283978 a(n) = A002487(n) - A283976(n) = (A002487(n) - A283977(n))/2.
%t A283978 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, 0, BitAnd[a[#], a[# + 1]] &[(n - 1)/2]], {n, 0, 120}] (* _Michael De Vlieger_, Mar 22 2017 *)
%o A283978 (Scheme) (define (A283978 n) (if (even? n) 0 (A004198bi (A002487 (/ (- n 1) 2)) (A002487 (/ (+ n 1) 2))))) ;; Where A004198bi implements bitwise-AND (A004198).
%o A283978 (PARI) A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
%o A283978 a(n) = if(n<2, 0, if(n%2, bitand(A(n\2), A((n + 1)/2)), 0));
%o A283978 for(n=0, 120, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 23 2017
%Y A283978 Bisections: A000004, A283988.
%Y A283978 Cf. A002487, A004198, A283976, A283977.
%K A283978 nonn,base
%O A283978 0,12
%A A283978 _Antti Karttunen_, Mar 21 2017