A283997 - OEIS

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A283997

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

5

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

(list; graph; refs; listen; history; text; internal format)

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