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

1,3

Comments

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

Links

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

Example

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   .           ...

Crossrefs

Cf. A337115

Sequence in context: A283072 A214599 A071066 * A137601 A232962 A158347

Adjacent sequences: A337365 A337366 A337367 * A337369 A337370 A337371

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Aug 25 2020

Status

approved