A368129 A variant of A367146 with application of the distance minimization to the second of two symmetrized versions of the strip bijection between two square lattices as described in A368126.

1, 8, 12, 24, 72, 156, 168, 216, 264, 624, 1560, 1752, 1836, 2232, 4824, 12456, 13080, 16380, 17064, 35040, 92184, 92952, 123096, 128844, 244584, 639192, 651432, 855240, 945756

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 1660752, 4293336, 4462104, 5787768, 6647916, 11050488, 28333080, 38414184, 45366204, 184427544.

Links

Table of n, a(n) for n=1..29.

Hugo Pfoertner, Example of one of the 8 islands in orbit with L=184427544.

Example

See files linked in A368130 for visualization of orbits.

Prog

(PARI) \\ Uses definitions and functions from
\\ a367150_PARI.txt and a368126_PARI.txt
cycle(v) = {my (n=1, w=BijectionD(v, Bijectionk)); while (w!=v, n++; w=BijectionD(w, Bijectionk)); n};
a368129(rmax=235) = {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};
a368129() \\ Terms < 1000, takes 5-10 minutes CPU time

Crossrefs

Cf. A307110, A367146, A367150, A368126.

A368130 is a permutation of this sequence.

A368124 is the analog for the first symmetrized version of the strip bijection.

Sequence in context: A241482 A368124 A349757 * A368130 A367894 A210982

Adjacent sequences: A368126 A368127 A368128 * A368130 A368131 A368132

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 03 2024

Status

approved