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A290780 Half-octavan primes: primes of the form (x^8 + y^8)/2.

%I A290780 #27 Aug 21 2017 03:09:10
%S A290780 198593,21523361,107182721,407865361,429388721,3487882001,11979660241,
%T A290780 39155495921,84785726833,141217650641,141321947681,250123401793,
%U A290780 253611085201,289278699121,391337974721,426445714033,426448401121
%N A290780 Half-octavan primes: primes of the form (x^8 + y^8)/2.
%H A290780 Charles R Greathouse IV, <a href="/A290780/b290780.txt">Table of n, a(n) for n = 1..10000</a>
%H A290780 A. J. C. Cunningham, <a href="/wiki/File:High_quartan_factorisations_and_primes.pdf">High quartan factorisations and primes</a>, Messenger of Mathematics 36 (1907), pp. 145-174.
%e A290780 a(1) = (5^8 + 3^8)/2 = 198593.
%e A290780 a(2) = (9^8 + 1^8)/2 = 21523361.
%e A290780 a(3) = (11^8 + 3^8)/2 = 107182721.
%e A290780 a(4) = (13^8 + 1^8)/2 = 407865361.
%e A290780 a(5) = (13^8 + 9^8)/2 = 429388721.
%p A290780 N:= 10^12: # to get all terms <= N
%p A290780 sort(convert(select(isprime, {seq(seq((x^8+y^8)/2, y= (x mod 2)..min(x,floor((2*N-x^8)^(1/8))),2),x=1..floor((2*N)^(1/8)))}),list)); # _Robert Israel_, Aug 21 2017
%t A290780 Sort[Select[Total/@(Union[Sort/@Tuples[Range[0, 50], 2]]^8)/2, PrimeQ]] (* or *) lst={};Do[If[PrimeQ[(a^8 + b^8) / 2], AppendTo[lst, (a^8 + b^8) / 2]], {a, 100}, {b, a, 100}]; Sort[lst] (* _Vincenzo Librandi_, Aug 21 2017 *)
%o A290780 (PARI) list(lim)=my(v=List(),x8,t); forstep(x=1,sqrtnint(lim\=1,8),2, x8=x^8; forstep(y=1,min(sqrtnint(lim-x8,8), x-1),2, if(isprime(t=(x8+y^8)/2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Aug 20 2017
%Y A290780 Cf. A006686, A002646.
%K A290780 nonn
%O A290780 1,1
%A A290780 _Charles R Greathouse IV_, Aug 20 2017