A063694 -id:A063694 - cp's OEIS frontend

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

Rémy Sigrist, Oct 27 2024

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.

			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

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Index entries for sequences related to binary expansion of n

See A063694, A063695 and A374355 for similar sequences.

Cf. A126684, A371459, A377414.

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); }

a(n) = 0 iff n belongs to A126684.
a(a(n)) = 0.
a(2*n) = 2*a(n).

A105186 Replace odd-positioned digits with 0 in ternary representation of n.

Original entry on oeis.org

0, 1, 2, 0, 1, 2, 0, 1, 2, 9, 10, 11, 9, 10, 11, 9, 10, 11, 18, 19, 20, 18, 19, 20, 18, 19, 20, 0, 1, 2, 0, 1, 2, 0, 1, 2, 9, 10, 11, 9, 10, 11, 9, 10, 11, 18, 19, 20, 18, 19, 20, 18, 19, 20, 0, 1, 2, 0, 1, 2, 0, 1, 2, 9, 10, 11, 9, 10, 11, 9, 10, 11, 18, 19, 20, 18, 19, 20, 18, 19, 20, 81, 82

Offset: 0

Reinhard Zumkeller, Apr 11 2005

			n = 123 = '11120' --> '10100' = 90 = a(123).

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A007089, A063694, A163325.

a105186 0 = 0
a105186 n = 9 * a105186 n' + mod t 3
            where (n', t) = divMod n 9
-- Reinhard Zumkeller, Sep 26 2015

a(n) = fromdigits(digits(n,9)%3,9); \\ Kevin Ryde, May 20 2020

a(n) = n - a(floor(n/3))*3, a(0) = 0.

a(n) = 9*a(floor(n/9)) + (n mod 9) mod 3. - Reinhard Zumkeller, Sep 26 2015

cp's OEIS Frontend

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

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