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

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

Author

Antti Karttunen, Mar 19 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. A004198, A005187, A283996, A283997.

Programs

Mathematica

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

PARI

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

Python

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

Scheme

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

Formula

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.