A122395 - OEIS

%I #9 Mar 12 2023 08:49:27

%S 3,5,7,17,19,31,41,53,109,127,271,293,499,811,929,2027,2161,3659,4373,

%T 4421,4969,8191,9311,10099,13121,13309,16001,17029,19181,22051,32579,

%U 38611,57839,72091,78607,93941,109229,128521,131071,143261,157211

%N Primes of the form p^k - p^(k-1) - 1, with p prime and k>1.

%C The paper by Stein and Williams gives a method for finding primes of this form when k>(p+1)/2.

%H Robert Israel, <a href="/A122395/b122395.txt">Table of n, a(n) for n = 1..10000</a>

%H Andreas Stein and H. C. Williams, <a href="https://doi.org/10.1090/S0025-5718-00-01212-6">Explicit primality criteria for (p-1)p^n-1</a>, Math. Comp. 69 (2000), 1721-1734.

%p N:= 10^6: # for terms <= N

%p p:= 1: R:= NULL:

%p do

%p   p:= nextprime(p);

%p   if p^2 - p - 1 > N then break fi;

%p   for k from 2 do

%p     q:= p^k - p^(k-1)-1;

%p     if q > N then break fi;

%p     if isprime(q) then R:= R, q fi;

%p od od:

%p sort(convert({R},list)); # _Robert Israel_, Mar 12 2023

%t nn=10^6; lst={}; n=1; While[p=Prime[n]; k=2; While[m=p^k-p^(k-1)-1; m<nn, If[PrimeQ[m], AppendTo[lst,m]]; k++ ]; k>2, n++ ]; lst=Union[lst]

%Y Cf. A122396.

%K nonn

%O 1,1

%A _T. D. Noe_, Aug 31 2006