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A367146
Cycle lengths obtained by repeated application of the distance-minimizing variant of the strip bijection for the square lattice described in A367150.
7
1, 8, 12, 24, 25, 56, 120, 152, 154, 200, 217, 376, 464, 568, 616, 1242, 1368, 1624, 1736, 1945, 4376, 4968, 5176, 10682, 13016, 14152, 15560, 17497, 40376, 42728, 46648, 94234, 120664, 125320, 139976, 157465, 367544, 376936, 419896, 840570, 1100760, 1119496, 1259720
OFFSET
1,2
COMMENTS
See the description in the similar A363760 for more information.
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