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

7, 11, 19, 43, 53, 67, 163, 211, 283, 331, 523, 547, 691, 787, 907, 1051, 1123, 1171, 1279, 1531, 1723, 1867, 2011, 2083, 2251, 2347, 2371, 2467, 2707, 2731, 2803, 2971, 3187, 3307, 3547, 3643, 3907, 3931, 4051, 4243, 4363, 4603, 4651, 4723, 5107, 5227

Offset: 1

Author

Vincenzo Librandi, May 12 2017

Keywords

• nonn
• easy

Examples

			a(1) = 2*(2^2)-1 = 7.
a(2) = 3*(2^2)-1 = 11.
a(3) = 5*(2^2)-1 = 19.
a(4) = 11*(2^2)-1 = 43.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2300

Crossrefs

Cf. A000312, A090866, A285015.

Programs

Mathematica

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&]

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

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