A296818 Squarefree values of k for which the quadratic field Q[ sqrt(k) ] possesses a norm-Euclidean ideal class.

-15, -11, -7, -5, -3, -2, -1, 2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 19, 21, 29, 33, 37, 41, 57, 73, 85

Offset

1,1

Comments

This generalizes A048981, because the unit ideal of a norm-Euclidean number field is a norm-Euclidean ideal. In other words, this sequence is the union of {-15, -5, 10, 15, 85} and A048981.

Links

Table of n, a(n) for n=1..26.

Kelly Emmrich and Clark Lyons, Norm-Euclidean Ideals in Galois Cubic Fields, Slides, West Coast Number Theory, Dec 18 2017.

H. W. Lenstra, Jr., Euclidean ideal classes, Soc. Math. France Astérisque, 1979, pp. 121-131.

Example

-5 is in the sequence because the ideal (2, 1+sqrt(-5)) is norm-Euclidean in the number field Q[ sqrt(-5) ].

Crossrefs

Cf. A003174, A048981.

Sequence in context: A013461 A013430 A131082 * A097953 A200522 A273445

Adjacent sequences: A296815 A296816 A296817 * A296819 A296820 A296821

Keyword

fini,sign,full,nice

Author

Robert C. Lyons, Dec 22 2017

Status

approved