%I #25 May 13 2017 00:53:51
%S 3,7,11,19,23,31,43,47,53,59,67,71,79,83,103,107,127,131,139,151,163,
%T 167,179,191,199,211,223,227,239,251,263,269,271,283,307,311,331,347,
%U 359,367,379,383,419,431,439,443,463,467,479,487,491,499,503,523,547
%N Primes of the form k * b^b - 1, with b > 1.
%C This sequence has relative density 1 - Prod_p 1-1/(p^p-p) = 0.52098749404893... in the primes, hence a(n) ~ kn log n where k = 1.91943... is the reciprocal of this quantity. - _Charles R Greathouse IV_, May 12 2017
%H Robert Israel, <a href="/A285015/b285015.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 1*(2^2)-1 = 3.
%e a(2) = 2*(2^2)-1 = 7.
%e a(9) = 2*(3^3)-1 = 53.
%p N:= 1000: # to get all terms <= N
%p bmax:= floor(ln(N+1)/LambertW(ln(N+1))):
%p sort(convert(select(isprime, {seq(seq(k*b^b-1, k=1..(N+1)/b^b),b=2..bmax)}),list)); # _Robert Israel_, May 11 2017
%t Take[Select[Union@Flatten@Table[k b^b - 1, {b, 2, 20}, {k, 148}], PrimeQ], 55]
%o (PARI) upto(n)=my(l=List([3]), b=2, s=1); n++; while(b^b < n, c = b^b; forstep(i=2, n\c, s, if(isprime(i*c-1), listput(l, i*c-1))); s=3-s; b++); listsort(l, 1); l \\ _David A. Corneth_, May 11 2017
%o (PARI) is(n)=if(!isprime(n), return(0)); my(t); forprime(p=2,, t=p^p; if((n+1)%t==0, return(1)); if(t>=n, return(0))) \\ _Charles R Greathouse IV_, May 11 2017
%Y Cf. A175768.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, May 08 2017