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%I #11 Nov 05 2017 21:01:28
%S 3,6563,72353,137633,787811,1745153,7444673,44726593,49202147,
%T 61503553,86093443,91858243,100006817,100072097,101686177,107444417,
%U 143046977,200006561,214756067,257412163,300452323,430372577,431661313,435812033,447149537,452523713,489805633,530372321,744340577
%N Primes which are the sum of three nonzero 8th powers.
%C Primes of form x^8 + y^8 + z^8 where x, y, z > 0.
%H Chai Wah Wu, <a href="/A283019/b283019.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 = 1^8 + 1^8 + 1^8;
%e 6563 = 1^8 + 1^8 + 3^8;
%e 72353 = 2^8 + 3^8 + 4^8, etc.
%t nn = 13; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^8)], # <= nn^8 && PrimeQ[#] &]
%o (PARI) list(lim)=my(v=List(),A,B,t); lim\=1; for(a=1,sqrtnint(lim-2,8), A=a^8; for(b=1,min(sqrtnint(lim-A-1,8),a), B=A+b^8; forstep(c=if(B%2,2,1),sqrtnint(lim-B,8),2, if(isprime(t=B+c^8), listput(v,t))))); Set(v) \\ _Charles R Greathouse IV_, Nov 05 2017
%Y Cf. A001016, A003381, A006686, A007490, A085317, A085318, A085319, A283017, A283018.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Feb 26 2017