A370427 a(n) is the least k >= 0 such that n OR k is a binary palindrome (where OR denotes the bitwise OR operator).

0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 5, 4, 3, 2, 1, 0, 1, 0, 9, 8, 1, 0, 9, 8, 3, 2, 1, 0, 3, 2, 1, 0, 1, 0, 17, 16, 9, 8, 25, 24, 5, 4, 21, 20, 1, 0, 17, 16, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 0, 33, 32, 17, 16, 49, 48, 1, 0, 33, 32, 17, 16, 49, 48

Offset: 0

Author

Rémy Sigrist, Feb 18 2024

Keywords

• nonn
• base
• easy
• look

Comments

The binary expansions of n and a(n) have no common 1's.

Examples

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

Links

• Paolo Xausa, Table of n, a(n) for n = 0..16383
• Rémy Sigrist, Scatterplot of (x, y) such that x OR y is a binary palindrome and x, y < 2^10
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to palindromes

Crossrefs

Cf. A006995, A030101, A175297, A344220 (XOR variant).

Programs

Mathematica

A370427[n_] := With[{r = IntegerReverse[n, 2]}, r - BitAnd[n, r]];
Array[A370427, 2^7, 0] (* Paolo Xausa, Feb 20 2024 *)

PARI

a(n) = my (r = fromdigits(Vecrev(binary(n)), 2)); r - bitand(n, r)

Formula

n AND a(n) = 0 (where AND denotes the bitwise AND operator).

a(n) = A030101(n) - (n AND A030101(n)).

a(n) = A030101(n) - A175297(n) (for any n > 0).

a(n) = 0 iff n belongs to A006995.