A377415 a(n) = n - A377414(n).

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

Offset

0,7

Comments

For any n > 0 with binary expansion (b_1 = 1, b_2, ..., b_k), the binary expansion of a(n) is (c_1, ..., c_k) where c_i = b_i when i is even, c_i = 0 when i is odd.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

a(n) = 0 iff n belongs to A126684.

a(a(n)) = 0.

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

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     0     101          0
   6     2     110         10
   7     2     111         10
   8     0    1000          0
   9     1    1001          1
  10     0    1010          0
  11     1    1011          1
  12     4    1100        100
  13     5    1101        101
  14     4    1110        100
  15     5    1111        101

Prog

(PARI) a(n) = { my (v = 0, x = exponent(n), y); while (n, n -= 2^y = exponent(n); if (x%2 != y%2, v += 2^y; ); ); return (v); }

Crossrefs

See A063694, A063695 and A374355 for similar sequences.

Cf. A126684, A371459, A377414.

Sequence in context: A112170 A366475 A259976 * A113685 A049825 A287443

Adjacent sequences: A377412 A377413 A377414 * A377416 A377417 A377418

Keyword

nonn,base,easy

Author

Rémy Sigrist, Oct 27 2024

Status

approved