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%I #22 Sep 08 2022 08:45:30
%S 3,5,19,31,367,389,431,2179,10667,13103,90397
%N Numbers n such that (11^n - 3^n)/8 is prime.
%C All terms are primes.
%C No other terms < 10^5.
%p A128027:=n->`if`(isprime((11^n-3^n)/8),n,NULL): seq(A128027(n),n=1..1000); # _Wesley Ivan Hurt_, Nov 19 2014
%t k=8; Select[ Prime[ Range[1,200] ], PrimeQ[ ((k+3)^# - 3^#)/k ]& ]
%t Do[If[PrimeQ[(11^n - 3^n)/8], Print[n]], {n, 10^4}] (* _Ryan Propper_, Mar 17 2007 *)
%t Select[Prime[Range[1200]], PrimeQ[(11^# - 3^#)/8] &] (* _Vincenzo Librandi_, Nov 20 2014 *)
%o (Magma) [p: p in PrimesUpTo(400) | IsPrime((11^p-3^p) div 8)]; // _Vincenzo Librandi_, Nov 20 2014
%o (PARI) is(n)=ispseudoprime((11^n - 3^n)/8) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A028491 = numbers n such that (3^n - 1)/2 is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128028, A128029, A128030, A128031, A128032.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Feb 11 2007
%E a(8) from _Ryan Propper_, Mar 17 2007
%E a(9) from _Farideh Firoozbakht_, Apr 04 2007
%E a(10)=13103, a(11)=90397 from _Robert Price_, Apr 24 2011
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