A257340 Arrange numbers in a single clockwise spiral so that each number is relatively prime to its four (N,S,E,W) neighbors.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 12, 17, 15, 14, 19, 16, 23, 18, 25, 22, 21, 20, 27, 26, 29, 24, 31, 35, 32, 37, 28, 41, 33, 34, 39, 40, 43, 30, 47, 36, 49, 38, 45, 44, 51, 46, 53, 42, 55, 48, 59, 50, 57, 61, 52, 63, 58, 65, 54, 67, 69, 56, 71, 62, 73

Offset: 1

Author

N. J. A. Sloane, Apr 21 2015

Keywords

• nonn

Comments

Start with 1; always choose smallest number which has not yet appeared.

It is conjectured that every number appears.

Examples

			.     |     -4 | -3 | -2 | -1 |  0 | +1 | +2 | +3 | +4 | +5
.  ---+--------+----+----+----+----+----+----+----+----+----
.     |
.     |   +------------------------------------------------
.  +4 |   | 83   68   75   74   81   70   87   76   85  ...
.  ---+   |    +---------------------------------------+
.  +3 |   | 66 | 49   38   45   44   51   46   53   42 |
.  ---+   |    |    +-----------------------------+    |
.  +2 |   | 79 | 36 | 25   22   21   20   27   26 | 55 |
.  ---+   |    |    |    +-------------------+    |    |
.  +1 |   | 64 | 47 | 18 |  7    8    9   10 | 29 | 48 |
.  ---+   |    |    |    |    +---------+    |    |    |
.   0 |   | 77 | 30 | 23 |  6 |  1    2 | 11 | 24 | 59 |
.  ---+   |    |    |    |    +----o    |    |    |    |
.  -1 |   | 60 | 43 | 16 |  5    4    3 | 13 | 31 | 50 |
.  ---+   |    |    |    +--------------+    |    |    |
.  -2 |   | 73 | 40 | 19   14   15   17   12 | 35 | 57 |
.  ---+   |    |    +------------------------+    |    |
.  -3 |   | 62 | 39   34   33   41   28   37   32 | 61 |
.  ---+   |    +----------------------------------+    |
.  -4 |   | 71   56   69   67   54   65   58   63   52 |
.  ---+   +--------------------------------------------+
.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A064413, A257321-A257339.

Extensions

More terms from Jon E. Schoenfield, Apr 23 2015