cp's OEIS Frontend

A285016 Primes of the form p*b^b - 1, where p is a prime and b>1.

%I A285016 #20 Jun 16 2022 14:28:30
%S A285016 7,11,19,43,53,67,163,211,283,331,523,547,691,787,907,1051,1123,1171,
%T A285016 1279,1531,1723,1867,2011,2083,2251,2347,2371,2467,2707,2731,2803,
%U A285016 2971,3187,3307,3547,3643,3907,3931,4051,4243,4363,4603,4651,4723,5107,5227
%N A285016 Primes of the form p*b^b - 1, where p is a prime and b>1.
%H A285016 Vincenzo Librandi, <a href="/A285016/b285016.txt">Table of n, a(n) for n = 1..2300</a>
%e A285016 a(1) = 2*(2^2)-1 = 7.
%e A285016 a(2) = 3*(2^2)-1 = 11.
%e A285016 a(3) = 5*(2^2)-1 = 19.
%e A285016 a(4) = 11*(2^2)-1 = 43.
%t A285016 nmax=10^4; pimax=PrimePi[nmax]; bmax=1;While[(bmax+1)^(bmax+1)<=nmax,bmax++]; Select[Union@Flatten@Table[Prime[pi] b^b-1,{b,2,bmax},{pi,pimax}],PrimeQ[#]&&#<=nmax&]
%o A285016 (PARI) is(n)=for(b=2,oo, my(B=b^b); if((n+1)%B==0 && isprime((n+1)/B), return(isprime(n))); if(2*B+1>n, return(0))) \\ _Charles R Greathouse IV_, Jun 16 2022
%o A285016 (PARI) list(lim)=my(v=List()); lim\=1; for(b=2,oo, my(p=2*b^b-1); if(p>lim, break); if(isprime(p), listput(v,p))); forstep(b=2,oo,2, my(B=b^b); if(3*B-1>lim, break); forprime(q=3,(lim+1)\B, my(p=q*B-1); if(isprime(p), listput(v,p)))); Set(v) \\ _Charles R Greathouse IV_, Jun 16 2022
%Y A285016 Cf. A000312, A090866, A285015.
%K A285016 nonn,easy
%O A285016 1,1
%A A285016 _Vincenzo Librandi_, May 12 2017