A283996 -id:A283996 - cp's OEIS frontend

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

Antti Karttunen, Mar 19 2017

Antti Karttunen, Table of n, a(n) for n = 0..8191
Index entries for sequences related to binary expansion of n

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

Cf. also A279357, A283477.

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

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

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

(define (A283997 n) (A003987bi n (A005187 (floor->exact (/ n 2))))) ;; Where A003987bi implements bitwise-XOR (A003987).

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)).

A283998 a(n) = n AND A005187(floor(n/2)), where AND is bitwise-and (A004198).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 4, 4, 0, 1, 8, 8, 8, 8, 10, 11, 0, 1, 16, 16, 16, 16, 18, 19, 16, 16, 18, 19, 24, 25, 26, 26, 0, 1, 32, 32, 32, 32, 34, 35, 32, 32, 34, 35, 40, 41, 42, 42, 32, 32, 34, 35, 48, 49, 50, 50, 48, 49, 50, 50, 56, 56, 56, 57, 0, 1, 64, 64, 64, 64, 66, 67, 64, 64, 66, 67, 72, 73, 74, 74, 64, 64, 66, 67, 80, 81, 82, 82, 80, 81, 82, 82, 88, 88, 88, 89

Offset: 0

Antti Karttunen, Mar 19 2017

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

Cf. A004198, A005187, A283996, A283997.

A[n_]:=2*n - DigitCount[2*n, 2, 1];Table[BitAnd[n, A[Floor[n/2]]], {n, 0, 100}] (* Indranil Ghosh, Mar 25 2017 *)

b(n) = if(n<1, 0, b(n\2) + n%2);
A(n) = 2*n - b(2*n);
for(n=0, 100, print1(bitand(n, A(floor(n/2))),", ")) \\ Indranil Ghosh, Mar 25 2017

def A(n): return 2*n - bin(2*n)[2:].count("1")
print([n&A(n//2) for n in range(101)]) # Indranil Ghosh, Mar 25 2017

(define (A283998 n) (A004198bi n (A005187 (floor->exact (/ n 2))))) ;; Where A004198bi implements bitwise-AND (A004198).

a(n) = n AND A005187(floor(n/2)), where AND is bitwise-and (A004198).
a(n) = A283996(n) - A283997(n).
a(n) = A005187(n) - A283996(n) = (A005187(n) - A283997(n))/2.

cp's OEIS Frontend

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

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