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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.

%I A367146 #14 Dec 14 2023 10:11:24
%S A367146 1,8,12,24,25,56,120,152,154,200,217,376,464,568,616,1242,1368,1624,
%T A367146 1736,1945,4376,4968,5176,10682,13016,14152,15560,17497,40376,42728,
%U A367146 46648,94234,120664,125320,139976,157465,367544,376936,419896,840570,1100760,1119496,1259720
%N A367146 Cycle lengths obtained by repeated application of the distance-minimizing variant of the strip bijection for the square lattice described in A367150.
%C A367146 See the description in the similar A363760 for more information.
%H A367146 Hugo Pfoertner, <a href="/A367146/a367146.txt">Examples of starting points for all known cycle lengths</a>, December 2023.
%H A367146 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/A367146_Orbits_Illustrations.pdf">Visualization of some selected orbits with lengths from L=24 to L=918330056</a>, December 2023.
%e A367146 a(1) = 1: D(0,0) -> [0,0];
%e A367146 a(2) = 8: [1,0] -> [1,1] -> [0,1] -> [-1,1] -> [-1,0] -> [-1,-1] -> [0,-1] -> [1,-1] -> [1,0];
%e A367146 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].
%e A367146 List of start points and corresponding cycle lengths:
%e A367146     y   0  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16
%e A367146    x \------------------------------------------------------------------
%e A367146    0 |  1  8  12   8   8   8   8   8   8  25   8   8   8   8   8  24   8
%e A367146    1 |  8  8  12   8   8   8   8   8   8 154   8   8   8   8   8  24   8
%e A367146    2 | 12 12   8   8   8   8   8  25  25 154 154   8   8   8   8   8  24
%e A367146    3 |  8  8   8   8   8   8  25  25   8   8 154 154 154 154   8   8   8
%e A367146    4 |  8  8   8   8   8   8   8  25   8   8 154   8   8   8 154   8   8
%e A367146    5 |  8  8   8   8   8   8   8 154 154 154 154   8   8   8 154   8 152
%e A367146    6 |  8  8   8   8   8   8   8  25   8   8 154   8   8   8 154 152   8
%e A367146    7 |  8  8  25  25  25  25 154   8   8   8   8 154 154 154   8 152   8
%e A367146    8 |  8  8  25   8   8 154   8   8   8   8   8   8   8   8   8 152   8
%e A367146    9 |154 25 154   8   8 154 154   8   8   8   8   8   8   8   8 152   8
%e A367146   10 |  8  8 154 154 154 154 154   8   8   8   8  24  24  24   8 152   8
%e A367146   11 |  8  8   8 154   8   8   8 154   8   8  24   8   8   8  24 152   8
%e A367146   12 |  8  8   8 154   8   8   8 154   8   8  24   8   8   8  24   8 152
%e A367146   13 |  8  8   8 154   8   8   8 154   8   8  24   8   8   8  24   8   8
%e A367146   14 |  8  8   8   8 154 154 154   8   8   8   8  24  24  24   8   8   8
%e A367146   15 | 24 24   8   8   8   8 152 152 152 152 152 152   8   8   8   8  24
%e A367146   16 |  8  8  24   8   8 152   8   8   8 152   8   8 152   8   8  24   8
%o A367146 (PARI) \\ It is assumed that the PARI program from A367150 has been loaded and the functions defined there are available.
%o A367146 cycle(v) = {my (n=1, w=BijectionD(v)); while (w!=v, n++; w=BijectionD(w)); n};
%o A367146 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};
%o A367146 a367146() \\ produces terms up to a(18)=1624 in about 5 minutes run time.
%Y A367146 Cf. A307110, A363760, A367150, A367894.
%K A367146 nonn
%O A367146 1,2
%A A367146 _Hugo Pfoertner_, Nov 25 2023