A368124 -id:A368124 - cp's OEIS frontend

A368121 A variant of A367150 with application of the distance minimization to an 8-fold symmetrically expanded sector between 0 and Pi/4 of the pair of rotated grids created by the strip bijection of A307110.

0, 5, 6, 7, 8, 2, 3, 4, 1, 13, 15, 17, 19, 14, 10, 16, 11, 18, 12, 20, 9, 26, 27, 28, 25, 21, 22, 23, 24, 38, 39, 40, 41, 42, 43, 44, 37, 30, 31, 32, 33, 34, 35, 36, 29, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 61, 46, 47, 48, 45, 50, 51, 52, 53, 54, 55, 56, 49, 70, 82, 72, 73, 84, 75, 76, 86, 78, 79, 88, 69, 71, 103

Offset: 0

Hugo Pfoertner, Jan 05 2024

Hugo Pfoertner, Table of n, a(n) for n = 0..10000
Klaus Nagel, Symmetrized strip bijection, with mirrored repetition of sector 0.
Hugo Pfoertner, Distance minimization applied to symmetrized strip bijection, using sector between 0 and Pi/4.
Hugo Pfoertner, PARI program.

A305575, A305576 are used for enumeration of the grid points.

Cf. A307110, A367150, A368124, A368125, A368126.

PARI
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\\ See Pfoertner link.
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A368125 A variant of A367894 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.

Original entry on oeis.org

1, 8, 12, 60, 24, 72, 300, 264, 216, 624, 168, 1692, 2232, 1752, 4824, 1560, 9804, 17064, 13080, 35040, 12456, 57084, 123096, 92952

Offset: 1

Hugo Pfoertner, Dec 31 2023

Hugo Pfoertner, Examples of points at minimum radius.
Hugo Pfoertner, Illustration of the orbits corresponding to the terms a(2)-a(24), (2024).

Cf. A307110, A367150, A367894, A368121.
A permutation of A368124.
A368130 is the analog for the second symmetrized version of the strip bijection.

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.

Original entry on oeis.org

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

Hugo Pfoertner, Jan 03 2024

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.

			See files linked in A368130 for visualization of orbits.

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

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.

\\ 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

cp's OEIS Frontend

A368121 A variant of A367150 with application of the distance minimization to an 8-fold symmetrically expanded sector between 0 and Pi/4 of the pair of rotated grids created by the strip bijection of A307110.

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PARI

A368125 A variant of A367894 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.

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Author

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Links

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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.

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PARI