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 A383048 #18 Aug 01 2025 19:28:10
%S A383048 2,5,6,11,14,15,17,23,26,29,31,33,35,38,41,42,47,51,53,59,62,65,69,71,
%T A383048 74,77,78,83,86,87,89,95,101,105,106,107,109,110,113,114,119,122,123,
%U A383048 129,131,134,137,141,143,146,149,155,158,159,161,167,170,173,174,177,179
%N A383048 Squarefree d such that x^3+y^3=z^3 has nontrivial solution in Q(sqrt(-d)).
%C A383048 Equivalent condition is that the elliptic curve dY^2=X^3+432 has positive rank.
%C A383048 If d == 1 (mod 3) appears in this sequence, 3 divides the class number of Q(sqrt(-d)).
%C A383048 For d not divisible by 3, d appears in this sequence if and only if 3d appears in A383047, and 3d appears in this sequence if and only if d appears in A383047.
%D A383048 M. Jones and J. Rouse, Solutions of the cubic Fermat equation in quadratic fields, Int. J. Number Theory 9 (2013), no. 6, 1579-1591.
%H A383048 Seiichi Azuma, <a href="/A383048/b383048.txt">Table of n, a(n) for n = 1..168</a>
%H A383048 M. Jones and J. Rouse, <a href="https://users.wfu.edu/rouseja/cv/jonesrouse.pdf">Solutions of the cubic Fermat equation in quadratic fields</a>.
%e A383048 For a(1)=2, (-2+sqrt(-2))^3+(-2-sqrt(-2))^3=2^3
%o A383048 (PARI) for(n=2,500,if(vecmax(factor(n)[,2])>= 2,next); r=ellrank(ellinit([0,0,0,0,432*n^3])); if(r[2]>0,print1(n, ", "); if(r[1]==0,print("uncertain!"))))
%Y A383048 Cf. A383047.
%K A383048 nonn
%O A383048 1,1
%A A383048 _Seiichi Azuma_, Apr 14 2025
%E A383048 a(50) corrected by _David Radcliffe_, Aug 01 2025