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 A166246 #12 Apr 23 2023 07:34:28
%S A166246 2,7,13,17,19,31,37,43,53,61,67,71,79,89,97,103,107,127,139,151,157,
%T A166246 163,179,193,197,211,223,229,233,241,251,269,271,277,283,313,331,337,
%U A166246 349,359,367,373,379,397,409,421,431,433,439,449,457,463,467,499,503,521
%N A166246 Primes representable as the sum of two rational cubes.
%C A166246 The prime elements of A159843, i.e., the intersection of A159843 and A000040.
%C A166246 Also, the prime elements of A020898.
%D A166246 H. Cohen, Number Theory. I, Tools and Diophantine Equations, Springer-Verlag, 2007, p. 378.
%H A166246 Fernando Rodriguez Villegas, Don Zagier, <a href="http://people.mpim-bonn.mpg.de/zagier/files/mpim/95-61/fulltext.pdf">Which primes are sums of two cubes?</a>, CMS Conference Proceedings 15 (1995), pp. 295-306.
%F A166246 Under the Birch and Swinnerton-Dyer conjecture, these primes consist of:
%F A166246 (i) p = 2;
%F A166246 (ii) p == 4, 7, or 8 (mod 9);
%F A166246 (iii) p == 1 (mod 9) and p divides A206309(p-1), i.e., Villegas-Zagier polynomial A166243((p-1)/3) evaluated at x=0.
%t A166246 (* To speed up computation, a few terms are pre-computed *) nmax = 521; xmax = 360; preComputed = {127, 271, 379}; solQ[p_] := Do[ If[ IntegerQ[z = Root[-x^3 - y^3 + p*#^3 & , 1]], Print[p, {x, y, z}]; Return[True]], {x, 2, xmax}, {y, x, xmax}]; A166246 = Union[ preComputed, Select[ Prime[ Range[ PrimePi[nmax]]], Mod[#, 9] == 4 || Mod[#, 9] == 7 || Mod[#, 9] == 8 || solQ[#] === True & ]](* _Jean-François Alcover_, Apr 04 2012, after given formula *)
%Y A166246 Cf. A166243, A166244, A159843.
%K A166246 nonn
%O A166246 1,1
%A A166246 _Max Alekseyev_, Oct 10 2009