A342217 The n-th and a(n)-th points of the Hilbert's Hamiltonian walk (A059252, A059253) are symmetrical with respect to the line X=Y.

0, 3, 2, 1, 14, 15, 12, 13, 8, 11, 10, 9, 6, 7, 4, 5, 58, 57, 56, 59, 60, 63, 62, 61, 50, 49, 48, 51, 52, 55, 54, 53, 32, 35, 34, 33, 46, 47, 44, 45, 40, 43, 42, 41, 38, 39, 36, 37, 26, 25, 24, 27, 28, 31, 30, 29, 18, 17, 16, 19, 20, 23, 22, 21, 234, 235, 232

Offset

0,2

Comments

In other words, a(n) is the unique k such that A059252(n) = A059253(k) and A059253(n) = A059252(k).

This sequence is a self-inverse permutation of the nonnegative integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..4095

Rémy Sigrist, PARI program for A342217

Index entries for sequences that are permutations of the nonnegative integers

Formula

a(n) = n iff n belongs to A062880.

a(n) < 16^k for any n < 16^k.

Example

The Hilbert's Hamiltonian walk (A059252, A059253) begins as follows:
     +     +-----+-----+
     |15   |12    11   |10
     |     |           |
     +-----+     +-----+
      14    13   |8     9
                 |
     +-----+     +-----+
     |1    |2     7    |6
     |     |           |
     +     +-----+-----+
      0     3     4     5
- so a(0) = 0,
     a(1) = 3,
     a(2) = 2,
     a(4) = 14,
     a(5) = 15,
     a(7) = 13,
     a(8) = 8,
     a(9) = 11,
     a(10) = 10.

Prog

(PARI) See Links section.

Crossrefs

See A342218 and A342224 for similar sequences.

Cf. A059252, A059253, A062880.

Sequence in context: A152405 A152400 A291978 * A111548 A140709 A109282

Adjacent sequences: A342214 A342215 A342216 * A342218 A342219 A342220

Keyword

nonn

Author

Rémy Sigrist, Mar 05 2021

Status

approved