A002157 - OEIS

%I M1317 N0505 #28 Oct 15 2023 13:15:37

%S 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 45,46,47,49,50,52,53,54,55,57,58,60,62,66,69,70,71,72,73,74,76,78,79,

%U 80,84,85,86,87,89,94,95,96,99,101,102,103,105,106,110,111,112,114,116

%N Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 (PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==1, print1(k", "))) \\ _Seiichi Manyama_, Jul 07 2019

%o (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 Cf. A060952.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms added by _Seiichi Manyama_, Jul 07 2019