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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.

%I A368124 #7 Jan 06 2024 23:00:01
%S A368124 1,8,12,24,60,72,168,216,264,300,624,1560,1692,1752,2232,4824,9804,
%T A368124 12456,13080,17064,35040,57084,92184,92952,123096,244584,332652,
%U A368124 639192,651432,855240,1660752
%N 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.
%C A368124 Apparently, a(n) == 0 (mod 4) for n > 1. For cycles, whose lengths are multiples of 8, the visited points form 8 separated islands.
%C A368124 Larger terms are 4293336, 4462104, 5787768, 11050488, 28333080, 38414184, 72397248.
%H A368124 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a368124_11050488.pdf">Example of one of the 8 islands in orbit with L=11050488</a>.
%H A368124 Hugo Pfoertner, <a href="https://www.randomwalk.de/sequences/a368125.pdf">Illustration of the orbits corresponding to the terms a(2)-a(24) of A368125</a>, (2024).
%o A368124 (PARI) \\ Uses definitions and functions from
%o A368124 \\ a367150_PARI.txt and a368121_PARI.txt
%o A368124 cycle(v) = {my (n=1, w=BijectionD(v, BijectionK)); while (w!=v, n++; w=BijectionD(w,BijectionK)); n};
%o A368124 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};
%o A368124 a368124() \\ Terms < 1000
%Y A368124 Cf. A307110, A367146, A367150, A368121.
%Y A368124 A368125 is a permutation of this sequence.
%Y A368124 A368129 is the analog for the second symmetrized version of the strip bijection.
%K A368124 nonn,more
%O A368124 1,2
%A A368124 _Hugo Pfoertner_, Jan 01 2024