

A342217


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


3



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
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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 selfinverse 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



