OFFSET
1,2
COMMENTS
See the description in the similar A363760 for more information.
LINKS
Hugo Pfoertner, Examples of starting points for all known cycle lengths, December 2023.
Hugo Pfoertner, Visualization of some selected orbits with lengths from L=24 to L=918330056, December 2023.
EXAMPLE
a(1) = 1: D(0,0) -> [0,0];
a(2) = 8: [1,0] -> [1,1] -> [0,1] -> [-1,1] -> [-1,0] -> [-1,-1] -> [0,-1] -> [1,-1] -> [1,0];
a(3) = 12: [2,0] -> [2,1] -> [1,2] -> [0,2] -> [-1,2] -> [-2,1] -> [-2,0] -> [-2,-1] -> [-1,-2] -> [0,-2] -> [1,-2] -> [2,-1] -> [2,0].
List of start points and corresponding cycle lengths:
y 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
x \------------------------------------------------------------------
0 | 1 8 12 8 8 8 8 8 8 25 8 8 8 8 8 24 8
1 | 8 8 12 8 8 8 8 8 8 154 8 8 8 8 8 24 8
2 | 12 12 8 8 8 8 8 25 25 154 154 8 8 8 8 8 24
3 | 8 8 8 8 8 8 25 25 8 8 154 154 154 154 8 8 8
4 | 8 8 8 8 8 8 8 25 8 8 154 8 8 8 154 8 8
5 | 8 8 8 8 8 8 8 154 154 154 154 8 8 8 154 8 152
6 | 8 8 8 8 8 8 8 25 8 8 154 8 8 8 154 152 8
7 | 8 8 25 25 25 25 154 8 8 8 8 154 154 154 8 152 8
8 | 8 8 25 8 8 154 8 8 8 8 8 8 8 8 8 152 8
9 |154 25 154 8 8 154 154 8 8 8 8 8 8 8 8 152 8
10 | 8 8 154 154 154 154 154 8 8 8 8 24 24 24 8 152 8
11 | 8 8 8 154 8 8 8 154 8 8 24 8 8 8 24 152 8
12 | 8 8 8 154 8 8 8 154 8 8 24 8 8 8 24 8 152
13 | 8 8 8 154 8 8 8 154 8 8 24 8 8 8 24 8 8
14 | 8 8 8 8 154 154 154 8 8 8 8 24 24 24 8 8 8
15 | 24 24 8 8 8 8 152 152 152 152 152 152 8 8 8 8 24
16 | 8 8 24 8 8 152 8 8 8 152 8 8 152 8 8 24 8
PROG
(PARI) \\ It is assumed that the PARI program from A367150 has been loaded and the functions defined there are available.
cycle(v) = {my (n=1, w=BijectionD(v)); while (w!=v, n++; w=BijectionD(w)); n};
a367146(rmax=205) = {my (L=List()); for (x=0, rmax, for(y=x, rmax, my(c=cycle([x, y])); if(setsearch(L, c)==0, listput(L, c); listsort(L, 1)))); L};
a367146() \\ produces terms up to a(18)=1624 in about 5 minutes run time.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Nov 25 2023
STATUS
approved