A283999 a(n) = A005187(n) XOR A006068(n), where XOR is bitwise-xor (A003987).

0, 0, 0, 6, 0, 14, 14, 14, 0, 30, 30, 30, 30, 30, 18, 16, 0, 62, 62, 62, 62, 62, 50, 48, 62, 62, 34, 32, 34, 32, 44, 44, 0, 126, 126, 126, 126, 126, 114, 112, 126, 126, 98, 96, 98, 96, 108, 108, 126, 126, 66, 64, 66, 64, 76, 76, 66, 64, 92, 92, 92, 92, 92, 82, 0, 254, 254, 254, 254, 254, 242, 240, 254, 254, 226, 224, 226, 224, 236, 236, 254, 254, 194, 192, 194

Offset: 0

Author

Antti Karttunen, Mar 20 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

Cf. A003987, A005187, A006068, A283997.

Programs

Mathematica

Table[BitXor[Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]], 2 n - DigitCount[2 n, 2, 1]], {n, 0, 84}] (* Michael De Vlieger, Mar 20 2017, after Jan Mangaldan at A006068 *)

PARI

b(n) = if(n<1, 0, b(n\2) + n%2);
A(n) = 2*n - b(2*n);
a(n) = if(n<2, n, 2*a(floor(n/2)) + (n%2 + a(floor(n/2))%2)%2);
for(n=0, 110, print1(bitxor(A(n),a(n)),", ")) \\ Indranil Ghosh, Mar 25 2017

Python

def A(n): return 2*n - bin(2*n)[2:].count("1")
def a(n): return n if n<2 else 2*a(n//2) + (n%2 + a(n//2)%2)%2
print([A(n)^a(n) for n in range(111)]) # Indranil Ghosh, Mar 25 2017

Scheme

(define (A283999 n) (A003987bi (A005187 n) (A006068 n))) ;; Where A003987bi implements bitwise-XOR (A003987).

Formula

a(n) = A005187(n) XOR A006068(n), where XOR is bitwise-xor (A003987).

a(n) = A006068(2*n) XOR A283997(2*n).