A337368 Spiral on a 2D square lattice, one term per cell, starting at the origin with 0; the four integers forming any 2 X 2 square have all digits 0 through 9 (with duplicate digits allowed).

0, 1, 2, 3456789, 3, 12, 4, 356789, 24, 5, 306789, 45, 6, 103789, 7, 102, 8, 45679, 80, 35679, 9, 1028, 10, 11, 306798, 13, 42, 14, 20, 13789, 15, 204, 25, 46, 3589, 467, 16, 20359, 17, 23, 41, 208, 18, 34567, 19, 34576, 289, 54, 21, 22, 4056789, 26, 305789, 36, 145, 206, 27, 3489, 67, 1389, 70, 112, 30

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Aug 25 2020

Keywords

• base
• nonn

Comments

This is defined to be the lexicographically earliest permutation of the nonnegative integers with this property.

Examples

			The spiral starts with the 2 X 2 square 0,1,2,A and this square contains all the digits 0 through 9 at least once; the upper right 2 X 2 square (here) has the same property —— and so have all the 2 X 2 squares of the grid.
.
      18———K——19———L——289—54———21——22           A = 3456789
       |                            |           B = 356789
     208   9———G——10——11———H———13  4056789      C = 306789
       |   |                   |    |           D = 103789
      41   F   4———B——24———5   42  26           E = 45679
       |   |   |           |   |    |           F = 35679
      23  80  12   0———1   C   14  305789       G = 1028
       |   |   |       |   |   |    |           H = 306798
      17   E   3———A———2  45   20  36           I = 3589
       |   |               |   |    .           J = 20359
       J   8——102——7———D———6  13789 .           K = 34567
       |                       |    .           L=  34576
      16——467——I——46——25——204——15   .           ...
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..3907

Crossrefs

Cf. A337115