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

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, 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, 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

Offset

0,12

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

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

a(n) = A283976(n) - A283977(n).

a(n) = A002487(n) - A283976(n) = (A002487(n) - A283977(n))/2.

Mathematica

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 *)

Prog

(Scheme) (define (A283978 n) (if (even? n) 0 (A004198bi (A002487 (/ (- n 1) 2)) (A002487 (/ (+ n 1) 2))))) ;; Where A004198bi implements bitwise-AND (A004198).
(PARI) A(n) = if(n<2, n, if(n%2, A(n\2) + A((n + 1)/2), A(n/2)));
a(n) = if(n<2, 0, if(n%2, bitand(A(n\2), A((n + 1)/2)), 0));
for(n=0, 120, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 23 2017

Crossrefs

Bisections: A000004, A283988.

Cf. A002487, A004198, A283976, A283977.

Sequence in context: A071957 A329186 A298609 * A002655 A064891 A278500

Adjacent sequences: A283975 A283976 A283977 * A283979 A283980 A283981

Keyword

nonn,base

Author

Antti Karttunen, Mar 21 2017

Status

approved