A065854 Smallest prime q such that (p^q-1)/(p-1) is a prime, where p = prime(n).

2, 3, 3, 5, 17, 5, 3, 19, 5, 5, 7, 13, 3, 5, 127, 11, 3, 7, 19, 3, 5, 5, 5, 3, 17, 3, 19, 17, 17, 23, 5, 3, 11, 163, 7, 13, 17, 7, 3, 3, 19, 17, 17, 5, 31, 577, 41, 239, 5, 11, 113, 5, 17, 7, 23, 5

Offset: 1

Author

Vladeta Jovovic, Nov 26 2001

Keywords

• hard
• nonn

Comments

a(n) = 2*A065813(n) + 1, n > 1.

Links

• Andy Steward, Titanic Prime Generalized Repunits

Crossrefs

Cf. A084740 (least k such that (n^k-1)/(n-1) is prime).

Programs

Mathematica

Do[p = Prime[n]; k = 1; While[ !PrimeQ[ (p^Prime[k] - 1)/(p - 1)], k++ ]; Print[ Prime[k]], {n, 1, 56} ]
Table[Module[{q=2},While[!PrimeQ[(p^q-1)/(p-1)],q=NextPrime[q]];q],{p,Prime[Range[60]]}] (* Harvey P. Dale, Aug 05 2025 *)

PARI

{ allocatemem(932245000); for (n=1, 100, p=prime(n); q=2; while (!isprime((p^q - 1)/(p - 1)), q=nextprime(q + 1)); write("b065854.txt", n, " ", q) ) } \\ Harry J. Smith, Nov 01 2009