A002152 Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 1. (Formerly M1065 N0401)

2, 4, 7, 13, 15, 18, 19, 20, 21, 22, 23, 25, 28, 29, 30, 35, 38, 40, 43, 44, 45, 48, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 63, 65, 66, 71, 72, 74, 75, 79, 81, 84, 85, 87, 91, 93, 94, 95, 100, 101, 102, 107, 110, 112, 115, 120, 123, 124, 126, 127, 128, 129, 130, 131, 135, 137

Offset

1,1

References

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

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

Links

Table of n, a(n) for n=1..66.

B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math., 212 (1963), 7-25.

Prog

(PARI) for(k=1, 200, if(ellanalyticrank(ellinit([0, 0, 0, 0, -k]))[1]==1, print1(k", "))) \\ Seiichi Manyama, Jul 06 2019
(Magma) for k in[1..200] do if Rank(EllipticCurve([0, 0, 0, 0, -k])) eq 1 then print k; end if; end for; // Vaclav Kotesovec, Jul 07 2019

Crossrefs

Sequence in context: A194422 A177101 A018414 * A163522 A255173 A002466

Adjacent sequences: A002149 A002150 A002151 * A002153 A002154 A002155

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Better definition from Artur Jasinski, Jun 30 2010

More terms added by Seiichi Manyama, Jul 06 2019

Status

approved