A368125 -id:A368125 - 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.
```

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.

Original entry on oeis.org

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

Hugo Pfoertner, Jan 01 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 4293336, 4462104, 5787768, 11050488, 28333080, 38414184, 72397248.

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).

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.

\\ 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

A368130 A variant of A367894 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, 156, 72, 216, 1836, 624, 168, 1752, 264, 16380, 4824, 1560, 13080, 2232, 128844, 35040, 12456, 92952, 17064, 945756, 244584

Offset: 1

Hugo Pfoertner, Dec 30 2023

Hugo Pfoertner, Examples of points at minimum radius.
Hugo Pfoertner, Illustration of the orbits corresponding to the terms a(2)-a(17), (2023).
Hugo Pfoertner, Illustration of the orbit with L=128844 corresponding to a(18), (2023).
Hugo Pfoertner, Illustration of the orbit with L=35040 corresponding to a(19), (2024).
Hugo Pfoertner, Illustration of the orbit with L=12456 corresponding to a(20), (2024).
Hugo Pfoertner, Illustration of the orbit with L=92952 corresponding to a(21), (2024).
Hugo Pfoertner, Illustration of the orbit with L=17064 corresponding to a(22), (2024).
Hugo Pfoertner, Illustration of the orbit with L=945756 corresponding to a(23), showing only every 11th visited point, (2024).
Hugo Pfoertner, Illustration of the orbit with L=244584 corresponding to a(24), showing only every 11th visited point, (2024).

Cf. A307110, A367150, A367894, A368126, A368129.
A permutation of A368129.
A368125 is the analog for the first symmetrized version of the strip bijection.

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

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.

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Author

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Links

Crossrefs

Programs

PARI

A368130 A variant of A367894 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.

Views

Author

Keywords

Links

Crossrefs