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 A166246 Primes representable as the sum of two rational cubes. 6
 2, 7, 13, 17, 19, 31, 37, 43, 53, 61, 67, 71, 79, 89, 97, 103, 107, 127, 139, 151, 157, 163, 179, 193, 197, 211, 223, 229, 233, 241, 251, 269, 271, 277, 283, 313, 331, 337, 349, 359, 367, 373, 379, 397, 409, 421, 431, 433, 439, 449, 457, 463, 467, 499, 503, 521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The prime elements of A159843, i.e., the intersection of A159843 and A000040. Also, the prime elements of A020898. REFERENCES H. Cohen, Number Theory. I, Tools and Diophantine Equations, Springer-Verlag, 2007, p. 378. LINKS FORMULA Under the Birch and Swinnerton-Dyer conjecture, these primes consist of: (i) p = 2; (ii) p == 4, 7, or 8 (mod 9); (iii) p == 1 (mod 9) and p divides A206309(p-1), i.e., Villegas-Zagier polynomial A166243((p-1)/3) evaluated at x=0. MATHEMATICA (* 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 *) CROSSREFS Cf. A166243, A166244, A159843. Sequence in context: A065104 A138645 A191060 * A250185 A063206 A063099 Adjacent sequences:  A166243 A166244 A166245 * A166247 A166248 A166249 KEYWORD nonn AUTHOR Max Alekseyev, Oct 10 2009 STATUS approved

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Last modified May 11 15:04 EDT 2021. Contains 343791 sequences. (Running on oeis4.)