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A283977 a(2n) = A002487(n), a(2n+1) = A002487(n) XOR A002487(n+1), where XOR is bitwise-xor (A003987). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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) = 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).

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 *)

PROG

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

(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

CROSSREFS

Bisections: A002487, A283987.

Cf. A003987, A283976, A283978.

Sequence in context: A200223 A236228 A082391 * A248579 A296992 A304783

Adjacent sequences:  A283974 A283975 A283976 * A283978 A283979 A283980

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Mar 21 2017

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)