%I #20 Aug 12 2024 14:48:28
%S 2,3,7,41,43,79,421
%N Numbers k such that ((2*k)^k - 1)/(2*k - 1) is prime.
%C The next k in the sequence is > 4261, if it exists.
%C Note that (b^k - 1)/(b-1) is prime only if k is prime, so all the elements in this sequence must be primes. - Marco Bodrato (marco2007(AT)bodrato.it), Oct 31 2007
%C a(8) > 20000, if it exists. - _Michael S. Branicky_, Aug 12 2024
%e (((2*2)^2) - 1)/(2*2 - 1) = 15/3 = 5 is prime so a(1)=2.
%t Select[Prime[Range[100]],PrimeQ[((2#)^#-1)/(2#-1)]&] (* _Harvey P. Dale_, Mar 09 2022 *)
%o (PARI) lista(nn) = {forprime(n = 2, nn, if (isprime(((2*n)^n-1)/(2*n-1)), print1(n, ", ")););} \\ _Michel Marcus_, Feb 05 2014
%Y Cf. A088790.
%K more,nonn
%O 1,1
%A _Pierre CAMI_, Jan 29 2005