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

1,2

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

Table of n, a(n) for n=1..31.

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).

Prog

(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

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.

Sequence in context: A328538 A077566 A241482 * A349757 A368129 A368130

Adjacent sequences: A368121 A368122 A368123 * A368125 A368126 A368127

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 01 2024

Status

approved