A322120 a(n) is the smallest composite k such that n^(k-1) == 1 (mod (n^2-1)*k).

341, 91, 91, 217, 481, 25, 65, 91, 91, 133, 133, 85, 781, 341, 91, 91, 25, 49, 671, 221, 169, 91, 553, 217, 133, 121, 361, 341, 49, 49, 25, 545, 703, 341, 403, 217, 85, 341, 121, 671, 529, 25, 703, 133, 133, 65, 481, 247, 793, 451, 671, 703, 361, 697, 403, 25

Offset: 2

Author

Thomas Ordowski, Nov 27 2018

Keywords

• nonn

Comments

a(n) >= A271801(n). All terms are odd and indivisible by 3.

Conjecture: if m is a composite number such that b^(m-1) == 1 (mod (b^2-1)m) for some b, then m is a strong pseudoprime to some base a in the range 2 <= a <= m-2. Thus, probably every term a(n) is in A181782.

Crossrefs

Cf. A181782, A271801, A298756, A322121.

Programs

Mathematica

a[n_] := Module[{k=4}, While[PrimeQ[k] || !Divisible[n^(k-1)-1, (n^2-1)k], k++]; k]; Array[a, 100, 2] (* Amiram Eldar, Nov 27 2018 *)

PARI

a(n) = {forcomposite(k=1, ,if (Mod(n, (n^2-1)*k)^(k-1) == 1, return (k)););} \\ Michel Marcus, Nov 28 2018

Extensions

More terms from Amiram Eldar, Nov 27 2018