A367146 Cycle lengths obtained by repeated application of the distance-minimizing variant of the strip bijection for the square lattice described in A367150.

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

Author

Hugo Pfoertner, Nov 25 2023

Keywords

• nonn

Comments

See the description in the similar A363760 for more information.

Examples

			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
		

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.

Crossrefs

Cf. A307110, A363760, A367150, A367894.

Programs

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.