A292272 a(n) = n - A048735(n) = n - (n AND floor(n/2)).

0, 1, 2, 2, 4, 5, 4, 4, 8, 9, 10, 10, 8, 9, 8, 8, 16, 17, 18, 18, 20, 21, 20, 20, 16, 17, 18, 18, 16, 17, 16, 16, 32, 33, 34, 34, 36, 37, 36, 36, 40, 41, 42, 42, 40, 41, 40, 40, 32, 33, 34, 34, 36, 37, 36, 36, 32, 33, 34, 34, 32, 33, 32, 32, 64, 65, 66, 66, 68, 69, 68, 68, 72, 73, 74, 74, 72, 73, 72, 72, 80, 81, 82, 82, 84, 85, 84, 84, 80, 81, 82, 82, 80, 81

Offset: 0

Author

Antti Karttunen, Sep 16 2017

Keywords

• nonn
• base

Comments

In binary expansion of n, change those 1's to 0's that have an 1-bit next to them at their left (more significant) side. Only fibbinary numbers (A003714) occur as terms.

Examples

			From _Kevin Ryde_, Jun 02 2020: (Start)
     n = 1831 = binary 11100100111
  a(n) = 1060 = binary 10000100100   high 1 of each run
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A003188, A003714, A003987, A004198, A005940, A048735, A085357, A292371, A292382.

Programs

Mathematica

Table[n - BitAnd[n, Floor[n/2]], {n, 0, 93}] (* Michael De Vlieger, Sep 17 2017 *)

PARI

a(n) = bitnegimply(n,n>>1); \\ Kevin Ryde, Jun 02 2020

Python

def A292272(n): return n&~(n>>1) # Chai Wah Wu, Jun 29 2022

Formula

a(n) = n - A048735(n) = n - (n AND floor(n/2)) = n XOR (n AND floor(n/2)), where AND is bitwise-AND (A004198) and XOR is bitwise-XOR (A003987).

a(n) = n AND A003188(n).

a(n) = A292382(A005940(1+n)).

A059905(a(n)) = A292371(n).

For all n >= 0, A085357(a(n)) = 1.

a(n) = A213064(n) / 2. - Kevin Ryde, Jun 02 2020

a(n) = n AND NOT floor(n/2). - Chai Wah Wu, Jun 29 2022