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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Mar 21 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Bisections: A002487, A283987.

Cf. A003987, A283976, A283978.

Programs

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, a[n/2], BitXor[a[#], a[# + 1]] &[(n - 1)/2]], {n, 0, 112}] (* Michael De Vlieger, Mar 22 2017 *)

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, n, if(n%2, bitxor(A(n\2), A((n + 1)/2)), A(n\2)));
for(n=0, 120, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 23 2017

Scheme

(define (A283977 n) (if (even? n) (A002487 n) (A003987bi (A002487 (/ (- n 1) 2)) (A002487 (/ (+ n 1) 2))))) ;; Where A003987bi implements bitwise-XOR (A003987).

Formula

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

a(n) = A283976(n) - A283978(n).

a(n) = A002487(n) - 2*A283978(n).