A342224 The n-th and a(n)-th points of the curve (A334474, A334475) are symmetrical with respect to the line X=Y.

0, 2, 1, 3, 8, 9, 7, 6, 4, 5, 15, 11, 14, 13, 12, 10, 31, 32, 30, 29, 33, 35, 34, 28, 27, 26, 25, 24, 23, 19, 18, 16, 17, 20, 22, 21, 63, 62, 59, 58, 60, 61, 42, 44, 43, 47, 46, 45, 57, 55, 56, 51, 54, 53, 52, 49, 50, 48, 39, 38, 40, 41, 37, 36, 121, 122, 120

Offset: 0

Author

Rémy Sigrist, Mar 06 2021

Keywords

• nonn

Comments

In other words, a(n) is the unique k such that A334474(n) = A334475(k) and A334474(k) = A334475(n).

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

Examples

			The curve (A334474, A334475) begins as follows on a hexagonal lattice:
                 +
                /5\
               /   \
              +4    +6
               \     \
                \     \
           +    3+     +7
          /1\   /     /
         /   \ /     /
        +     +     +----+
         0     2     8    9
- so a(0) = 0,
     a(1) = 2,
     a(3) = 3,
     a(4) = 8,
     a(5) = 9,
     a(6) = 7.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8255
• Rémy Sigrist, PARI program for A342224
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A342217 and A342218 for similar sequences.

Cf. A007582, A334474, A334475.

Programs

PARI

See Links section.

Formula

a(n) < A007582(k) for any n < A007582(k).