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%I #30 Sep 08 2022 08:45:14
%S 41,313,1201,7321,14281,41761,97241,139921,353641,750313,1156721,
%T 5278001,6922921,8925313,12705841,14199121,21523361,56275441,60775313,
%U 81523681,87450313,100266961,138461441,273990641,370600313,407865361
%N Primes of the form (n^4 + 1)/2.
%C Note that n must be odd. Terms of primitive Pythagorean triples: (n^2, (n^4-1)/2, (n^4+1)/2).
%H Charles R Greathouse IV, <a href="/A096170/b096170.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=41 because (3^4 + 1)/2 = 82/2 = 41 is prime.
%t Select[(Range[200]^4+1)/2,PrimeQ] (* _Harvey P. Dale_, Mar 09 2013 *)
%o (Magma) [ a: n in [0..2500] | IsPrime(a) where a is ((n^4+1) div 2) ]; // _Vincenzo Librandi_, Apr 15 2011
%o (PARI) list(lim)=my(v=List(),t); forstep(n=3,sqrtnint(lim\1*2-1,4),2, if(isprime(t=(n^4+1)/2), listput(v,t))); Vec(v) \\ _Charles R Greathouse IV_, Feb 14 2017
%Y Cf. A096169 (n^4+1)/2 is prime, A000068 n^4+1 is prime, A037896 primes of the form n^4+1, A096171 n^4+1 is an odd semiprime, A096172 largest prime factor of n^4+1.
%K nonn
%O 1,1
%A _Hugo Pfoertner_, Jun 19 2004
%E Name edited by _Zak Seidov_, Apr 14 2011
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