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Numbers k such that ((2*k)^k - 1)/(2*k - 1) is prime.
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%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