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%I #8 Jan 18 2017 20:20:11
%S 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,
%T 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,
%U 23,5
%N Smallest prime q such that (p^q-1)/(p-1) is a prime, where p = prime(n).
%C a(n) = 2*A065813(n) + 1, n > 1.
%H Andy Steward, <a href="http://www.users.globalnet.co.uk/~aads/titans.html">Titanic Prime Generalized Repunits</a>
%t Do[p = Prime[n]; k = 1; While[ !PrimeQ[ (p^Prime[k] - 1)/(p - 1)], k++ ]; Print[ Prime[k]], {n, 1, 56} ]
%o (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
%Y Cf. A084740 (least k such that (n^k-1)/(n-1) is prime).
%K hard,nonn
%O 1,1
%A _Vladeta Jovovic_, Nov 26 2001