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

0,7

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Formula

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

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

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

Example

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

Prog

(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); }

Crossrefs

Cf. A000120, A265263.

Sequence in context: A363623 A376630 A101565 * A292944 A327188 A330270

Adjacent sequences: A377401 A377402 A377403 * A377405 A377406 A377407

Keyword

nonn,base,easy

Author

Rémy Sigrist, Oct 28 2024

Status

approved