This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384439 #17 Jun 03 2025 15:17:21
%S A384439 23,13,59,79,97,139,163,223,151,283,251,257,263,277,227,463,271,373,
%T A384439 587,457,641,461,499,389,503,683,761,673,509,523,709,631,757,619,571,
%U A384439 691,929,727
%N A384439 a(n) is the smallest prime p such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = p^3, where 0 < x < y < z < w has exactly n positive integer solutions.
%C A384439 a(39) > 4027 if it exists. - _Chai Wah Wu_, Jun 03 2025
%H A384439 Chai Wah Wu, <a href="/A384439/a384439.txt">All terms <= 4007</a>.
%e A384439 a(3)=59, because 59^3 = 13^3 + 21^3 + 41^3 + 50^3 = 14^3 + 19^3 + 44^3 + 48^3 = 21^3 + 23^3 + 26^3 + 55^3 and no prime less than 59 has 3 solutions.
%t A384439 Table[SelectFirst[Table[{Length@Select[PowersRepresentations[p^3,4,3],#[[4]]>#[[3]]>#[[2]]>#[[1]]>0&],p},{p,Prime@Range@25}],#[[1]]==k&],{k,5}]
%Y A384439 Cf. A377372, A383877.
%K A384439 nonn,more
%O A384439 1,1
%A A384439 _Zhining Yang_, May 29 2025