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%I A002157 M1317 N0505 #28 Oct 15 2023 13:15:37
%S A002157 2,5,6,7,10,12,14,15,20,21,22,23,25,26,30,31,32,34,36,37,38,39,41,42,
%T A002157 45,46,47,49,50,52,53,54,55,57,58,60,62,66,69,70,71,72,73,74,76,78,79,
%U A002157 80,84,85,86,87,89,94,95,96,99,101,102,103,105,106,110,111,112,114,116
%N A002157 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.
%D A002157 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002157 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002157 B. J. Birch and H. P. F. Swinnerton-Dyer, <a href="https://eudml.org/doc/150565">Notes on elliptic curves, I</a>, J. Reine Angew. Math., 212 (1963), 7-25.
%o A002157 (PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==1, print1(k", "))) \\ _Seiichi Manyama_, Jul 07 2019
%o A002157 (Magma) for k in[1..200] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 1 then print k; end if; end for; // _Vaclav Kotesovec_, Jul 07 2019
%Y A002157 Cf. A060952.
%K A002157 nonn
%O A002157 1,1
%A A002157 _N. J. A. Sloane_
%E A002157 More terms added by _Seiichi Manyama_, Jul 07 2019

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