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.

1, 10, 12, 56, 110, 37, 278, 60, 398, 72, 36, 154, 1114, 370, 2336, 168, 614, 444, 516, 1786, 192, 660, 600, 1128, 84, 156, 120, 2952, 492, 1574, 961, 3456, 2100, 10790, 564, 2604, 12110, 10440, 1500, 3924, 4882, 25570, 1668, 16524, 1164, 12876, 9610, 9420, 22906, 7008, 10716

Offset: 1

Author

Hugo Pfoertner, Dec 08 2023

Keywords

• nonn

Examples

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

Links

• Hugo Pfoertner, Examples of points at minimum radius.
• Hugo Pfoertner, Illustration of all cycles with minimum radius up to 700. Zoom into the images to see details, e.g., the green line that connects every 12th point visited.

Crossrefs

A permutation of A367148.

Cf. A367147.

Programs

PARI

\\ Bijection function Q provided in A367147
cycle(v, upto=oo)= {my (n=1, w=Q(v)); while (w!=v, n++; if (n>upto,return(0)); w=Q(w)); n};
\\ upto can be used to ignore longer cycles
a367149(Points, upto=oo) =
{ my (L=LL=List());
  for (n=1, #Points,
       my (c=cycle(Points[n],upto));
       if (c>0 && setsearch(LL,c)==0,
       \\ deactivate print to mute diagnostic printout
       print ([c, Points[n], sqrt(Points[n][1]^2 + Points[n][2]^2 + Points[n][1] *Points[n][2])]);
       listput(L,c);
       listput(LL,c); listsort(LL,1))
      ); L};
\\ Function a307014_16 provided in A307014
\\ Enumeration of grid points of triangular lattice by increasing radius
Plist = a307014_16(120,-46); \\ creates list of 52218 grid points
a367149(Plist) \\ all cycles having a point with R < 120 (a(1)-a(28)); takes 2 to 4 minutes