login
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.
2
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
1,2
LINKS
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.
EXAMPLE
See the linked file with list of points at minimum radius.
PROG
(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
CROSSREFS
A permutation of A367148.
Cf. A367147.
Sequence in context: A248481 A266700 A242508 * A363285 A219917 A257039
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Dec 08 2023
STATUS
approved