A283997 a(n) = n XOR A005187(floor(n/2)), where XOR is bitwise-xor (A003987).

0, 1, 3, 2, 7, 6, 2, 3, 15, 14, 2, 3, 6, 7, 5, 4, 31, 30, 2, 3, 6, 7, 5, 4, 14, 15, 13, 12, 5, 4, 4, 5, 63, 62, 2, 3, 6, 7, 5, 4, 14, 15, 13, 12, 5, 4, 4, 5, 30, 31, 29, 28, 5, 4, 4, 5, 13, 12, 12, 13, 4, 5, 7, 6, 127, 126, 2, 3, 6, 7, 5, 4, 14, 15, 13, 12, 5, 4, 4, 5, 30, 31, 29, 28, 5, 4, 4, 5, 13, 12, 12, 13, 4, 5, 7, 6, 62, 63, 61, 60, 5, 4, 4, 5, 13, 12, 12

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

a(n) = n XOR A005187(floor(n/2)), where XOR is bitwise-xor (A003987).

a(n) = A283996(n) - A283998(n).

a(n) = A005187(n) - 2*A283998(n).

a(n) = A006068(n) XOR A283999(floor(n/2)).

Mathematica

Table[BitXor[n, 2 # - DigitCount[2 #, 2, 1] &@ Floor[n/2]], {n, 0, 106}] (* Michael De Vlieger, Mar 20 2017 *)

Prog

(Scheme) (define (A283997 n) (A003987bi n (A005187 (floor->exact (/ n 2))))) ;; Where A003987bi implements bitwise-XOR (A003987).
(PARI) b(n) = if(n<1, 0, b(n\2) + n%2);
A(n) = 2*n - b(2*n);
for(n=0, 110, print1(bitxor(n, A(floor(n/2))), ", ")) \\ Indranil Ghosh, Mar 25 2017
(Python)
def A(n): return 2*n - bin(2*n)[2:].count("1")
print([n^A(n//2) for n in range(111)]) # Indranil Ghosh, Mar 25 2017

Crossrefs

Cf. A003986, A005187, A006068, A283996, A283998, A283999.

Cf. also A279357, A283477.

Sequence in context: A033318 A093780 A101307 * A096899 A265345 A340447

Adjacent sequences: A283994 A283995 A283996 * A283998 A283999 A284000

Keyword

nonn,base,hear

Author

Antti Karttunen, Mar 19 2017

Status

approved