A279191 Primes p such that L(p^2) = (p-1)*L(p)/4, where L(i) = A279186(i).

53, 61, 97, 113, 149, 193, 349, 389, 461, 769, 773, 857, 941

Offset: 1

Author

N. J. A. Sloane, Dec 14 2016

Keywords

• nonn
• more

Links

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

Crossrefs

Cf. A279185, A279186, A279187, A279188, A279189, A279190, A279192.

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]/4, Print[p]]] (* Jean-François Alcover, Oct 07 2018, after Robert Israel in A279186 *)

Extensions

a(8)-a(13) from Jean-François Alcover, Oct 07 2018