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A367149 Length of cycles obtained by repeated application of the strip bijection for the triangular lattice (A367147), sorted by increasing minimum radius visited by any cycle of this length.

%I A367149 #10 Jan 14 2024 20:33:47
%S A367149 1,10,12,56,110,37,278,60,398,72,36,154,1114,370,2336,168,614,444,516,
%T A367149 1786,192,660,600,1128,84,156,120,2952,492,1574,961,3456,2100,10790,
%U A367149 564,2604,12110,10440,1500,3924,4882,25570,1668,16524,1164,12876,9610,9420,22906,7008,10716
%N A367149 Length of cycles obtained by repeated application of the strip bijection for the triangular lattice (A367147), sorted by increasing minimum radius visited by any cycle of this length.
%H A367149 Hugo Pfoertner, <a href="/A367149/a367149.txt">Examples of points at minimum radius</a>.
%H A367149 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a367149.pdf">Illustration of all cycles with minimum radius up to 700</a>. Zoom into the images to see details, e.g., the green line that connects every 12th point visited.
%e A367149 See the linked file with list of points at minimum radius.
%o A367149 (PARI) \\ Bijection function Q provided in A367147
%o A367149 cycle(v, upto=oo)= {my (n=1, w=Q(v)); while (w!=v, n++; if (n>upto,return(0)); w=Q(w)); n};
%o A367149 \\ upto can be used to ignore longer cycles
%o A367149 a367149(Points, upto=oo) =
%o A367149 { my (L=LL=List());
%o A367149   for (n=1, #Points,
%o A367149        my (c=cycle(Points[n],upto));
%o A367149        if (c>0 && setsearch(LL,c)==0,
%o A367149        \\ deactivate print to mute diagnostic printout
%o A367149        print ([c, Points[n], sqrt(Points[n][1]^2 + Points[n][2]^2 + Points[n][1] *Points[n][2])]);
%o A367149        listput(L,c);
%o A367149        listput(LL,c); listsort(LL,1))
%o A367149       ); L};
%o A367149 \\ Function a307014_16 provided in A307014
%o A367149 \\ Enumeration of grid points of triangular lattice by increasing radius
%o A367149 Plist = a307014_16(120,-46); \\ creates list of 52218 grid points
%o A367149 a367149(Plist) \\ all cycles having a point with R < 120 (a(1)-a(28)); takes 2 to 4 minutes
%Y A367149 A permutation of A367148.
%Y A367149 Cf. A367147.
%K A367149 nonn
%O A367149 1,2
%A A367149 _Hugo Pfoertner_, Dec 08 2023