This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367150 #15 Dec 22 2024 10:50:49 %S A367150 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, %T A367150 22,23,24,38,39,40,41,42,43,44,37,30,31,32,33,34,35,36,29,57,58,59,60, %U A367150 62,63,64,65,66,67,68,61,46,47,48,45,50,51,52,53,54,55 %N A367150 Results of the strip bijection as described in A307110 with subsequent reassignment of the pair connections at all locations, in which 4 points of a unit square in one grid are mapped to a unit square in the other (rotated by Pi/4) grid in such a way that the maximum distance of the two points in the 4 assigned pairs is minimized. %C A367150 The strip bijection of A307110 assigns each grid point in one grid to a unique grid point in the rotated grid. The mapping therefore corresponds to a permutation of the nonnegative integers. Approximately 2/3 of the grid points are mapped in such a way that 4 points that form a unit square in the original grid also form a unit square after being mapped onto the rotated grid. We call this a stable (grid) cell under the bijection map. The method differs from that used in A307731 in that for each stable cell it is tried whether the maximum of the 4 pair distances resulting from the application of strip bijection can be reduced by a cyclic rotation of the connections. The one of the two assignments by cyclic connection change is selected that provides a smaller maximum of the 4 distances in the pairs assigned to each other. In contrast, a cyclic rotation of the connections is only carried out in the method of A307731 if the maximum of the 4 distances exceeds the upper limit of the bijection distance of sqrt(5)*sin(Pi/8)=0.855706... . %H A367150 Hugo Pfoertner, <a href="/A367150/b367150.txt">Table of n, a(n) for n = 0..10001</a> %H A367150 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a367150_PARI.txt">PARI program</a>. %H A367150 Rainer Rosenthal and Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/A367150vsA307110.pdf">A367150 compared to A307110</a>. %e A367150 n i = A305575(n) %e A367150 | | j = A305576(n) %e A367150 | | | A307110(n) %e A367150 | | | | k m distance_A307110 %e A367150 | | | | | | | a(n) k' m' distance after %e A367150 | | | | | | | | | | reconnecting %e A367150 0 0 0 0 0 0 0.0000 0 0 0 0.0000 %e A367150 1 1 0 1 1 0 0.7654 L 5 1 1 0.4142 r %e A367150 2 0 1 6 -1 1 0.4142 6 -1 1 0.4142 %e A367150 3 -1 0 3 -1 0 0.7654 L 7 -1 -1 0.4142 r %e A367150 4 0 -1 8 1 -1 0.4142 8 1 -1 0.4142 %e A367150 5 1 1 2 0 1 0.4142 2 0 1 0.4142 %e A367150 6 -1 1 11 -2 0 0.5858 3 -1 0 0.4142 r %e A367150 7 -1 -1 4 0 -1 0.4142 4 0 -1 0.4142 %e A367150 8 1 -1 9 2 0 0.5858 1 1 0 0.4142 r %e A367150 9 2 0 5 1 1 0.5858 13 2 1 0.7174 r %e A367150 10 0 2 15 -1 2 0.7174 15 -1 2 0.7174 %e A367150 11 -2 0 7 -1 -1 0.5858 17 -2 -1 0.7174 r %e A367150 13 2 1 improved by reconnecting %e A367150 15 -1 2 L = 0.7654 -> 0.7174 %e A367150 17 -2 -1 %e A367150 See the linked file for a visualization of the differences from A307110. %o A367150 (PARI) \\ See Pfoertner link. %Y A367150 Cf. A305575, A305576 (enumeration of the grid points in the square lattice). %Y A367150 Cf. A307110, A307731, A367146, A367895, A367896. %K A367150 nonn %O A367150 0,2 %A A367150 _Rainer Rosenthal_ and _Hugo Pfoertner_, Nov 22 2023