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

1,2

Comments

See the description in the similar A363760 for more information.

Links

Table of n, a(n) for n=1..43.

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

Cf. A307110, A363760, A367150, A367894.

Sequence in context: A141616 A368549 A326994 * A278902 A336583 A333754

Adjacent sequences: A367143 A367144 A367145 * A367147 A367148 A367149

Keyword

nonn

Author

Hugo Pfoertner, Nov 25 2023

Status

approved