A367894 -id:A367894 - cp's OEIS frontend

A368125 A variant of A367894 with application of the distance minimization to the first of two symmetrized versions of the strip bijection between two square lattices as described in A368121.

1, 8, 12, 60, 24, 72, 300, 264, 216, 624, 168, 1692, 2232, 1752, 4824, 1560, 9804, 17064, 13080, 35040, 12456, 57084, 123096, 92952

Offset: 1

Hugo Pfoertner, Dec 31 2023

Hugo Pfoertner, Examples of points at minimum radius.
Hugo Pfoertner, Illustration of the orbits corresponding to the terms a(2)-a(24), (2024).

Cf. A307110, A367150, A367894, A368121.
A permutation of A368124.
A368130 is the analog for the second symmetrized version of the strip bijection.

A368130 A variant of A367894 with application of the distance minimization to the second of two symmetrized versions of the strip bijection between two square lattices as described in A368126.

Original entry on oeis.org

1, 8, 12, 24, 156, 72, 216, 1836, 624, 168, 1752, 264, 16380, 4824, 1560, 13080, 2232, 128844, 35040, 12456, 92952, 17064, 945756, 244584

Offset: 1

Hugo Pfoertner, Dec 30 2023

Hugo Pfoertner, Examples of points at minimum radius.
Hugo Pfoertner, Illustration of the orbits corresponding to the terms a(2)-a(17), (2023).
Hugo Pfoertner, Illustration of the orbit with L=128844 corresponding to a(18), (2023).
Hugo Pfoertner, Illustration of the orbit with L=35040 corresponding to a(19), (2024).
Hugo Pfoertner, Illustration of the orbit with L=12456 corresponding to a(20), (2024).
Hugo Pfoertner, Illustration of the orbit with L=92952 corresponding to a(21), (2024).
Hugo Pfoertner, Illustration of the orbit with L=17064 corresponding to a(22), (2024).
Hugo Pfoertner, Illustration of the orbit with L=945756 corresponding to a(23), showing only every 11th visited point, (2024).
Hugo Pfoertner, Illustration of the orbit with L=244584 corresponding to a(24), showing only every 11th visited point, (2024).

Cf. A307110, A367150, A367894, A368126, A368129.
A permutation of A368129.
A368125 is the analog for the first symmetrized version of the strip bijection.

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

Original entry on oeis.org

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

Hugo Pfoertner, Nov 25 2023

nonn

See the description in the similar A363760 for more information.

			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

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.

Cf. A307110, A363760, A367150, A367894.

\\ 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.

cp's OEIS Frontend

A368125 A variant of A367894 with application of the distance minimization to the first of two symmetrized versions of the strip bijection between two square lattices as described in A368121.

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A368130 A variant of A367894 with application of the distance minimization to the second of two symmetrized versions of the strip bijection between two square lattices as described in A368126.

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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.

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