A368124 A variant of A367146 with application of the distance minimization to the first of two symmetrized versions of the strip bijection between two square lattices as described in A368121.

1, 8, 12, 24, 60, 72, 168, 216, 264, 300, 624, 1560, 1692, 1752, 2232, 4824, 9804, 12456, 13080, 17064, 35040, 57084, 92184, 92952, 123096, 244584, 332652, 639192, 651432, 855240, 1660752

Offset: 1

Author

Hugo Pfoertner, Jan 01 2024

Keywords

• nonn
• more

Comments

Apparently, a(n) == 0 (mod 4) for n > 1. For cycles, whose lengths are multiples of 8, the visited points form 8 separated islands.

Larger terms are 4293336, 4462104, 5787768, 11050488, 28333080, 38414184, 72397248.

Links

• Hugo Pfoertner, Example of one of the 8 islands in orbit with L=11050488.
• Hugo Pfoertner, Illustration of the orbits corresponding to the terms a(2)-a(24) of A368125, (2024).

Crossrefs

Cf. A307110, A367146, A367150, A368121.

A368125 is a permutation of this sequence.

A368129 is the analog for the second symmetrized version of the strip bijection.

Programs

PARI

\\ Uses definitions and functions from
\\ a367150_PARI.txt and a368121_PARI.txt
cycle(v) = {my (n=1, w=BijectionD(v, BijectionK)); while (w!=v, n++; w=BijectionD(w,BijectionK)); n};
a368124(rmax=205) = {my (L=List()); for (r2=0, rmax^2, for (x=0, sqrtint(r2), my (y2=r2-x^2,y); if (issquare(y2,&y), if(x>=y, my (c=cycle([x,y])); if (setsearch(L,c)==0, print([c,[x,y],sqrt(x^2+y^2)],", "); listput(L,c); listsort(L,1)))))); L};
a368124() \\ Terms < 1000