A361146 a(n) is the sibling of n in the infinite binary tree underlying A361144.

2, 1, 9, 5, 4, 7, 6, 10, 3, 8, 14, 31, 18, 11, 17, 19, 15, 13, 16, 21, 20, 23, 22, 26, 32, 24, 28, 27, 30, 29, 12, 25, 34, 33, 41, 37, 36, 39, 38, 42, 35, 40, 133, 46, 50, 44, 49, 51, 47, 45, 48, 53, 52, 56, 59, 54, 76, 60, 55, 58, 62, 61, 64, 63, 66, 65, 73

Offset: 1

Author

Rémy Sigrist, Mar 02 2023

Keywords

• nonn

Comments

This sequence is a self-inverse permutation of the positive integers with no fixed point.

Examples

			The infinite binary tree underlying A361144 starts as follows:
                                176
                 ---------------------------------
                43                              133
         -----------------               -----------------
        12              31              57              76
     ---------       ---------       ---------       ---------
     3       9      13      18      25      32      35      41
   -----   -----   -----   -----   -----   -----   -----   -----
   1   2   4   5   6   7   8  10  11  14  15  17  16  19  20  21
.
So a(1) = 2 and a(2) = 1, a(4) = 5 and a(5) = 4, etc.,
   a(3) = 9 and a(9) = 3, a(13) = 18 and a(18) = 13, etc.,
   a(12) = 31 and a(31) = 12, a(57) = 76 and a(76) = 57,
   a(43) = 133 and a(133) = 43.
		

Links

• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A328654, A361144.

Programs

PARI

See Links section.

Formula

a(A361144(2*n)) = A361144(2*n-1).

a(A361144(2*n-1)) = A361144(2*n).