A253279 Arrange numbers in a clockwise spiral with initial terms a(1)=1, a(2)=2, a(4)=3, a(6)=4, a(8)=5; thereafter each number shares a factor with each of its four (N,S,E,W) neighbors.

1, 2, 6, 3, 12, 4, 10, 5, 20, 8, 14, 16, 18, 9, 15, 21, 7, 28, 22, 24, 26, 30, 25, 35, 40, 32, 34, 36, 38, 42, 27, 33, 39, 45, 48, 56, 44, 70, 46, 50, 52, 13, 65, 60, 51, 75, 55, 66, 54, 57, 72, 58, 62, 64, 68, 78, 63, 69, 81, 84, 80, 74, 76, 82, 41

Offset: 1

Author

Vladimir Shevelev, May 02 2015

Keywords

• nonn

Comments

Start with smallest number which has not yet appeared and satisfies the conditions: a(3)=6; thereafter always choose smallest number which has not yet appeared and satisfies the conditions.

This is a two-dimensional spiral analog of EKG sequence A064413.

In A064413 we have initial terms in the positions 1,2.

In the two-dimensional case we have 4 sides.

So the initial TERMS are

5

4 1 2 (1)

3

But the POSITIONS in the spiral are indexed thus:

.

7--8--9--10

|

6 1--2

| |

5--4--3

.

So the initial terms, by (1), are a(1)=1, a(2)=2, a(4)=3, a(6)=4, a(8)=5.

Conjecture: The sequence is a permutation of the positive integers. - Vladimir Shevelev, May 06 2015

Examples

			The spiral begins
.
   26--30--25--35--40--32  etc.
    |
   24  10---5--20---8
    |   |           |
   22   4   1---2  14
    |   |       |   |
   28  12---3---6  16
    |               |
    7--21--15---9--18
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5625
• Peter J. C. Moses, The first few squares.

Crossrefs

Cf. A064413, A257321-A257340, A257112.

Extensions

Correction of a(42) and more terms from Peter J. C. Moses, May 03 2015