A337368 - OEIS

%I #15 Aug 30 2020 01:28:07

%S 0,1,2,3456789,3,12,4,356789,24,5,306789,45,6,103789,7,102,8,45679,80,

%T 35679,9,1028,10,11,306798,13,42,14,20,13789,15,204,25,46,3589,467,16,

%U 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

%N 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).

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

%H Jean-Marc Falcoz, <a href="/A337368/b337368.txt">Table of n, a(n) for n = 1..3907</a>

%e 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.

%e .

%e       18———K——19———L——289—54———21——22           A = 3456789

%e        |                            |           B = 356789

%e      208   9———G——10——11———H———13  4056789      C = 306789

%e        |   |                   |    |           D = 103789

%e       41   F   4———B——24———5   42  26           E = 45679

%e        |   |   |           |   |    |           F = 35679

%e       23  80  12   0———1   C   14  305789       G = 1028

%e        |   |   |       |   |   |    |           H = 306798

%e       17   E   3———A———2  45   20  36           I = 3589

%e        |   |               |   |    .           J = 20359

%e        J   8——102——7———D———6  13789 .           K = 34567

%e        |                       |    .           L=  34576

%e       16——467——I——46——25——204——15   .           ...

%Y Cf. A337115

%K base,nonn

%O 1,3

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 25 2020