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

1,2

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, Table of n, a(n) for n = 1..5625

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

Cf. A064413, A257321-A257340, A257112.

Sequence in context: A298480 A353916 A370501 * A355212 A297076 A304752

Adjacent sequences: A253276 A253277 A253278 * A253280 A253281 A253282

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