A283976 a(2n) = A002487(n), a(2n+1) = A002487(n) OR A002487(n+1), where OR is bitwise-or (A003986).

0, 1, 1, 1, 1, 3, 2, 3, 1, 3, 3, 3, 2, 3, 3, 3, 1, 5, 4, 7, 3, 7, 5, 7, 2, 7, 5, 7, 3, 7, 4, 5, 1, 5, 5, 5, 4, 7, 7, 7, 3, 11, 8, 13, 5, 7, 7, 7, 2, 7, 7, 7, 5, 13, 8, 11, 3, 7, 7, 7, 4, 5, 5, 5, 1, 7, 6, 7, 5, 13, 9, 13, 4, 15, 11, 15, 7, 15, 10, 11, 3, 11, 11, 11, 8, 13, 13, 13, 5, 13, 12, 15, 7, 15, 9, 11, 2, 11, 9, 15, 7, 15, 12, 13, 5, 13, 13, 13, 8

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, A283986.

Cf. A002487, A003986, A283977, 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], BitOr[a[#], a[# + 1]] &[(n - 1)/2]], {n, 0, 108}] (* 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, bitor(A(n\2), A((n + 1)/2)), A(n\2)));
for(n=0, 101, print1(a(n),", ")) \\ Indranil Ghosh, Mar 23 2017

Scheme

(define (A283976 n) (if (even? n) (A002487 n) (A003986bi (A002487 (/ (- n 1) 2)) (A002487 (/ (+ n 1) 2))))) ;; Where A003986bi implements bitwise-OR (A003986).

Formula

a(2n) = A002487(2n) = A002487(n), a(2n+1) = A002487(n) OR A002487(n+1), where OR is bitwise-or (A003986).

a(n) = A283977(n) + A283978(n).

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