A367149 - OEIS

%I #10 Jan 14 2024 20:33:47

%S 1,10,12,56,110,37,278,60,398,72,36,154,1114,370,2336,168,614,444,516,

%T 1786,192,660,600,1128,84,156,120,2952,492,1574,961,3456,2100,10790,

%U 564,2604,12110,10440,1500,3924,4882,25570,1668,16524,1164,12876,9610,9420,22906,7008,10716

%N 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 Hugo Pfoertner, <a href="/A367149/a367149.txt">Examples of points at minimum radius</a>.

%H 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 See the linked file with list of points at minimum radius.

%o (PARI) \\ Bijection function Q provided in A367147

%o cycle(v, upto=oo)= {my (n=1, w=Q(v)); while (w!=v, n++; if (n>upto,return(0)); w=Q(w)); n};

%o \\ upto can be used to ignore longer cycles

%o a367149(Points, upto=oo) =

%o { my (L=LL=List());

%o   for (n=1, #Points,

%o        my (c=cycle(Points[n],upto));

%o        if (c>0 && setsearch(LL,c)==0,

%o        \\ deactivate print to mute diagnostic printout

%o        print ([c, Points[n], sqrt(Points[n][1]^2 + Points[n][2]^2 + Points[n][1] *Points[n][2])]);

%o        listput(L,c);

%o        listput(LL,c); listsort(LL,1))

%o       ); L};

%o \\ Function a307014_16 provided in A307014

%o \\ Enumeration of grid points of triangular lattice by increasing radius

%o Plist = a307014_16(120,-46); \\ creates list of 52218 grid points

%o a367149(Plist) \\ all cycles having a point with R < 120 (a(1)-a(28)); takes 2 to 4 minutes

%Y A permutation of A367148.

%Y Cf. A367147.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Dec 08 2023