OFFSET
1,2
COMMENTS
To formulate the additional condition, let us call two numbers strictly connected if the set of prime divisors of one of them is a subset of the set of prime divisors of the other. Then the positions of two strictly connected terms should not be a knight's move apart.
Start with smallest number which has not yet appeared and satisfies the conditions: a(3)=11; thereafter always choose smallest number which has not yet appeared and satisfies the conditions.
This is a two-dimensional spiral analog of A098550.
In A098550 we have initial terms in the positions 1,2,3.
In the two-dimensional case we have 4 sides. So the initial TERMS are
9
8
7 6 1 2 3 (1)
4
5
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)=4, a(6)=6, a(8)=8, ...
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
.
21---32----9---28---27---10 etc.
|
22 25----8--165---14
| | |
7 6 1----2 3
| | | |
18 55----4---11 16
| |
35---12----5---26---15
.
Formally the smallest a(12) is 10, but then 10 and 5 are strictly connected numbers on a knight move (and a(13) would not exist). So the smallest suitable a(12)=16.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 24 2015
EXTENSIONS
More terms from Peter J. C. Moses, Apr 29 2015
STATUS
approved