%I #18 Mar 07 2021 14:41:18

%S 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,

%T 48,51,52,55,54,53,32,35,34,33,46,47,44,45,40,43,42,41,38,39,36,37,26,

%U 25,24,27,28,31,30,29,18,17,16,19,20,23,22,21,234,235,232

%N 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.

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

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

%H Rémy Sigrist, <a href="/A342217/b342217.txt">Table of n, a(n) for n = 0..4095</a>

%H Rémy Sigrist, <a href="/A342217/a342217.gp.txt">PARI program for A342217</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>

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

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

%e The Hilbert's Hamiltonian walk (A059252, A059253) begins as follows:

%e + +-----+-----+

%e |15 |12 11 |10

%e | | |

%e +-----+ +-----+

%e 14 13 |8 9

%e |

%e +-----+ +-----+

%e |1 |2 7 |6

%e | | |

%e + +-----+-----+

%e 0 3 4 5

%e - so a(0) = 0,

%e a(1) = 3,

%e a(2) = 2,

%e a(4) = 14,

%e a(5) = 15,

%e a(7) = 13,

%e a(8) = 8,

%e a(9) = 11,

%e a(10) = 10.

%o (PARI) See Links section.

%Y See A342218 and A342224 for similar sequences.

%Y Cf. A059252, A059253, A062880.

%K nonn

%O 0,2

%A _Rémy Sigrist_, Mar 05 2021