A377372 - OEIS

%I #14 Jan 11 2025 19:14:05

%S 2,19,41,479,1031,1181,577,2999,10711,29033,24919

%N a(n) is the smallest prime p such that the Diophantine equation x^3 + y^3 + z^3 = p^3, where 0 < x <= y <= z has exactly n positive integer solutions.

%e a(3)=479, because 479^3 = 47^3 +350^3 + 406^3 = 109^3 + 293^3 + 437^3= 256^3 + 311^3 + 398^3 and no prime less than 479 has 3 solutions.

%t a = Table[SelectFirst[Table[{p,Length@Select[PowersRepresentations[p^3, 3, 3], #[[1]] > 0 &]}, {p, Prime@Range@200}], #[[2]] == k &], {k, 0, 6}]

%Y Cf. A316359, A377444.

%K nonn,more

%O 0,1

%A _Zhining Yang_, Dec 28 2024