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%I #13 Aug 11 2023 10:00:34
%S 3,83,113,163,353,593,787,1553,2593,3217,4993,5393,6563,6833,7187,
%T 7793,7873,8273,8963,9043,9587,10337,11953,13697,14177,14723,14753,
%U 16193,17123,20753,21283,21377,21617,23603,25457,26561,27763,28643,28723
%N Primes which are the sum of three positive 4th powers.
%H Donovan Johnson, <a href="/A085318/b085318.txt">Table of n, a(n) for n = 1..10000</a>
%e 113 = 81+16+16 is in the sequence.
%t Select[Prime@ Range[2^12], And[Length[#] > 0, AnyTrue[#, AllTrue[#, # > 0 &] &]] &@ PowersRepresentations[#, 3, 4] &] (* _Michael De Vlieger_, Aug 10 2023 *)
%o (PARI) lista(nn) = {v = vector(nn, i, i^4); w = vector(0); for (i=1, nn, for (j=1, nn, for (k=1, nn, w = Set(concat(w, v[i]+v[j]+v[k]));););); for (i=1, #w, if (isprime(wp=w[i]) && (wp < vecmax(v)), print1(wp, ", ")););} \\ _Michel Marcus_, Dec 19 2013
%Y Cf. A003337.
%K nonn
%O 1,1
%A _Labos Elemer_, Jul 01 2003