%I
%S 9043,17863,32801,40787,43669,50599,62417,76099,101267,104149,107777,
%T 135893,160073,164419,249107,249857,256609,259733,266663,340649,
%U 348833,365639,430343,504061,545843,554663,604649,627901,640949,762743,776183
%N Primes which are the sum of 3 distinct positive 5th powers.
%C Intersection of the A000040 with the sequence 276, 1057, 1268, 1299, 3158,... of sums of 3 distinct positive 5th powers. [_R. J. Mathar_, Jun 18 2009]
%H Harvey P. Dale, <a href="/A161610/b161610.txt">Table of n, a(n) for n = 1..5000</a>
%e 9043=6^5+4^5+3^5. 17863=7^5+4^5+2^5. 32801=8^5+2^5+1^5. 40787=8^5+6^5+3^5, 43669=8^5+6^5+5^5.
%t lst={};Do[Do[Do[p=n^5+m^5+k^5;If[PrimeQ[p],AppendTo[lst,p]],{n,m+1,3*4!}], {m,k+1,6!}],{k,2*6!}];Take[Union[lst],5! ]
%t Module[{upto=10^6},Select[Total/@Subsets[Range[Ceiling[Surd[upto,5]]]^5,{3}], PrimeQ[#]&&#<=upto&]]//Union (* _Harvey P. Dale_, May 01 2019 *)
%Y Cf. A085319, A003348.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 14 2009
