A377404 In the binary expansion of n, replace the first, third, fifth, etc. 1's by 0's.

0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 4, 4, 4, 5, 0, 1, 2, 2, 4, 4, 4, 5, 8, 8, 8, 9, 8, 9, 10, 10, 0, 1, 2, 2, 4, 4, 4, 5, 8, 8, 8, 9, 8, 9, 10, 10, 16, 16, 16, 17, 16, 17, 18, 18, 16, 17, 18, 18, 20, 20, 20, 21, 0, 1, 2, 2, 4, 4, 4, 5, 8, 8, 8, 9, 8, 9, 10, 10

Offset: 0

Author

Rémy Sigrist, Oct 28 2024

Keywords

• nonn
• base
• easy

Comments

Each 1 in the binary expansion of n appears either in a(n) or in A265263(n).

Examples

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     0       1          0
   2     0      10          0
   3     1      11          1
   4     0     100          0
   5     1     101          1
   6     2     110         10
   7     2     111         10
   8     0    1000          0
   9     1    1001          1
  10     2    1010         10
  11     2    1011         10
  12     4    1100        100
  13     4    1101        100
  14     4    1110        100
  15     5    1111        101
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A265263.

Programs

PARI

a(n) = { my (b = binary(n), h = 0); for (i = 1, #b, if (b[i] && h++%2==1, b[i]
= 0;);); fromdigits(b, 2); }

Formula

a(n) = n - A265263(n).

a(2*n) = 2*a(n).

A000120(a(n)) = floor(A000120(n)/2).