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 A279189 #15 Feb 03 2024 10:17:18
%S A279189 2,3,5,29,179,293,317,467,509,659,797,1427,1949,2213,2339,2579,2909,
%T A279189 3677,4157,4229,4253,4349,5309,5573,5693,5843,5939,6173,6269,6653,
%U A279189 6899,6947,7043,7517,7589,8387,8573,8819,9059,9533,10067,10163,10259,10589,11069,11549,11939,13763,14627,15443
%N A279189 Primes p such that L(p^2) = (p-1)*L(p), where L(i) = A279186(i).
%C A279189 Also, union of {2} and the primes p from A001122 such that gcd(p-1,A007733(p-1)) = 1. - _Max Alekseyev_, Feb 02 2024
%H A279189 Haifeng Xu, <a href="http://arxiv.org/abs/1601.06509">The largest cycles consist by the quadratic residues and Fermat primes</a>, arXiv:1601.06509 [math.NT], 2016.
%t A279189 T[n_, k_] := Module[{g, y, r}, If[k == 0, Return[1]]; y = n; g = GCD[k, y]; While[g > 1, y = y/g; g = GCD[k, y]]; If[y == 1, Return[1]]; r = MultiplicativeOrder[k, y]; r = r/2^IntegerExponent[r, 2]; If[r == 1, Return[1]]; MultiplicativeOrder[2, r]];
%t A279189 L[n_] := L[n] = Table[T[n, k], {k, 0, n - 1}] // Max;
%t A279189 For[p = 2, p < 1000, p = NextPrime[p], If[L[p^2] == (p-1) L[p], Print[p]]] (* _Jean-François Alcover_, Oct 07 2018, after _Robert Israel_ in A279186 *)
%Y A279189 Excluding a(1)=2, forms a subsequence of A001122.
%Y A279189 Cf. A279185, A279186, A279187, A279188.
%K A279189 nonn
%O A279189 1,1
%A A279189 _N. J. A. Sloane_, Dec 14 2016
%E A279189 a(8)-a(11) from _Jean-François Alcover_, Oct 07 2018
%E A279189 Terms a(12) onward from _Max Alekseyev_, Feb 02 2024