A342218 The n-th and a(n)-th points of the Peano curve (A163528, A163529) are symmetrical with respect to the line X=Y.

0, 5, 6, 7, 4, 1, 2, 3, 8, 45, 50, 51, 52, 49, 46, 47, 48, 53, 54, 59, 60, 61, 58, 55, 56, 57, 62, 63, 68, 69, 70, 67, 64, 65, 66, 71, 36, 41, 42, 43, 40, 37, 38, 39, 44, 9, 14, 15, 16, 13, 10, 11, 12, 17, 18, 23, 24, 25, 22, 19, 20, 21, 26, 27, 32, 33, 34, 31

Offset: 0

Author

Rémy Sigrist, Mar 05 2021

Keywords

• nonn
• look

Comments

In other words, a(n) is the unique k such that A163528(n) = A163529(k) and A163528(k) = A163529(n).

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

Examples

			The Peano curve (A163528, A163529) begins as follows:
       +-----+-----+
       |6     7     8
       |
       +-----+-----+
        5     4    |3
                   |
       +-----+-----+
        0     1     2
- so a(0) = 0,
     a(1) = 5,
     a(2) = 6,
     a(3) = 7,
     a(4) = 4,
     a(8) = 8.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Rémy Sigrist, PARI program for A342218
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

See A342217 and A342224 for similar sequences.

Cf. A163528, A163529, A338086.

Programs

PARI

See Links section.

PARI

my(table=[0,5,6,7,4,1,2,3,8]); a(n) = fromdigits(apply(d->table[d+1], digits(n,9)), 9); \\ Kevin Ryde, Mar 07 2021

Formula

a(n) = n iff n belongs to A338086.

a(n) < 9^k for any n < 9^k.