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%I #10 Mar 09 2017 16:53:13
%S 3,857,1459,4889,50753,51481,66377,119107,210961,262937,308801,525017,
%T 531569,539633,562691,766739,797681,840241,1000793,1046657,1078507,
%U 1772291,1864873,2303003,2834443,2986777,3032641,3107729,3365777,4757609,4804201,5135609,5987593,7530329,7534361,7743529,8061041
%N Primes which are the sum of three nonzero 6th powers.
%C Primes of form x^6 + y^6 + z^6 where x, y, z > 0.
%H Robert Israel, <a href="/A283017/b283017.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 = 1^6 + 1^6 + 1^6;
%e 857 = 2^6 + 2^6 + 3^6;
%e 1459 = 1^6 + 3^6 + 3^6, etc.
%p N:= 10^8: # to get all terms <= N
%p S:= [seq(i^6, i=1..floor(N^(1/6)))]:
%p S3:= {seq(seq(seq(S[i]+S[j]+S[k],k=1..j),j=1..i),i=1..nops(S))}:
%p sort(convert(select(t -> t <= N and isprime(t), S3), list)); # _Robert Israel_, Mar 09 2017
%t nn = 15; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^6)], # <= nn^6 && PrimeQ[#] &]
%o (PARI) list(lim)=my(v=List(),a6,a6b6,t); lim\=1; for(a=1,sqrtnint(lim-2,6), a6=a^6; for(b=1,min(sqrtnint(lim-a6-1,6),a), a6b6=a6+b^6; forstep(c=if(a6b6%2,2,1),min(sqrtnint(lim-a6b6,6),b),2, if(isprime(t=a6b6+c^6), listput(v,t))))); Set(v) \\ _Charles R Greathouse IV_, Mar 09 2017
%Y Cf. A001014, A003359, A007490, A085317, A085318, A085319, A283018, A283019.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Feb 26 2017
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