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Numbers n such that 4*nextprime(2^n)^2+1 is prime.
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%I #8 Dec 27 2014 11:08:47

%S 0,1,2,5,6,18,43,52,106,383,417,663,849,971

%N Numbers n such that 4*nextprime(2^n)^2+1 is prime.

%C This sequence provides "simplest" examples of large primes of the form x^2+1, cf. A174246.

%e a(1)=0 since nextprime(2^0)=2 and 4*2^2+1 = 17 is prime.

%t fQ[n_] := PrimeQ[ 4NextPrime[2^n]^2 + 1]; Select[ Range@ 3000, fQ] (* _Robert G. Wilson v_, Dec 27 2014 *)

%o (PARI) for(n=0,9e9,ispseudoprime(4*nextprime(2^n)^2+1)&&print1(n","))

%Y Cf. A174246.

%K nonn

%O 1,3

%A _M. F. Hasler_, Oct 12 2014

%E a(13) and a(14) from _Robert G. Wilson v_, Dec 27 2014