A279189 Primes p such that L(p^2) = (p-1)*L(p), where L(i) = A279186(i).

2, 3, 5, 29, 179, 293, 317, 467, 509, 659, 797, 1427, 1949, 2213, 2339, 2579, 2909, 3677, 4157, 4229, 4253, 4349, 5309, 5573, 5693, 5843, 5939, 6173, 6269, 6653, 6899, 6947, 7043, 7517, 7589, 8387, 8573, 8819, 9059, 9533, 10067, 10163, 10259, 10589, 11069, 11549, 11939, 13763, 14627, 15443

Offset: 1

Author

N. J. A. Sloane, Dec 14 2016

Keywords

• nonn

Comments

Also, union of {2} and the primes p from A001122 such that gcd(p-1,A007733(p-1)) = 1. - Max Alekseyev, Feb 02 2024

Links

• Haifeng Xu, The largest cycles consist by the quadratic residues and Fermat primes, arXiv:1601.06509 [math.NT], 2016.

Crossrefs

Excluding a(1)=2, forms a subsequence of A001122.

Cf. A279185, A279186, A279187, A279188.

Programs

Mathematica

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]];
L[n_] := L[n] = Table[T[n, k], {k, 0, n - 1}] // Max;
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 *)

Extensions

a(8)-a(11) from Jean-François Alcover, Oct 07 2018

Terms a(12) onward from Max Alekseyev, Feb 02 2024