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%I #32 Sep 08 2022 08:45:19
%S 3,5,15,25,55,125,205,385,465,635,645,715,1095,1145,1175,1245,1275,
%T 1315,1375,1565,1615,1675,1685,1965,2055,2085,2095,2405,2455,2535,
%U 2665,2835,2925,3135,3305,3535,3755,3775,4025,4155,4175,4365,4605,4615,4735,4785
%N Numbers k such that k^4 + 4 is semiprime.
%C Except for the first, all the terms above generate brilliant numbers.
%C Numbers n such that n - 1 + i and n + 1 + i are (twin) Gaussian primes, see Shanks. - _Charles R Greathouse IV_, Apr 20 2011
%H Amiram Eldar, <a href="/A108814/b108814.txt">Table of n, a(n) for n = 1..10000</a>
%H Daniel Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1960-0111724-0">A Note on Gaussian Twin Primes</a>, Mathematics of Computation 14:70 (1960), pp. 201-203.
%F a(k) = A096012(k) + 1. (Because n^4+4 = ((n-1)^2+1)((n+1)^2+1).) - _Jeppe Stig Nielsen_, Feb 26 2016
%t Select[Range[5000],PrimeOmega[#^4+4]==2&] (* _Harvey P. Dale_, Sep 07 2017 *)
%o (PARI) forstep(n=1,1e5,2,if(isprime(n^2-2*n+2) && isprime(n^2+2*n+2), print1(n", "))) \\ _Charles R Greathouse IV_, Apr 20 2011
%o (Magma) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [1..5000] | IsSemiprime(n^4+4)]; // _Vincenzo Librandi_, Apr 20 2011
%Y Cf. A001358, A057781, A096012.
%K nonn
%O 1,1
%A _Jason Earls_, Jul 10 2005