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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.
6
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
1,2
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
LINKS
Peter J. C. Moses, The first few squares.
EXAMPLE
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 02 2015
EXTENSIONS
Correction of a(42) and more terms from Peter J. C. Moses, May 03 2015
STATUS
approved