A263465 Values of D for which the imaginary quadratic field Q[ sqrt(-D) ] is norm-Euclidean.

1, 2, 3, 7, 11

Offset

1,2

Comments

Hardy & Wright's Theorem 246: "There are just five complex Euclidean quadratic fields, viz., ... ."

References

P. M. Cohn, On the structure of the GL2 of a ring, Publ. Math. Inst. Hautes Etudes Sci., 30 (1966), 5-53.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 5th ed., Oxford Univ. Press, 1979, p. 213.

Links

Table of n, a(n) for n=1..5.

Bogdan Nica, The Unreasonable Slightness of E2 over Imaginary Quadratic Rings, Amer. Math. Monthly, 118 (2011), 455-462.

Arseniy Sheydvasser, A Corrigendum to Unreasonable Slightness, Amer. Math. Monthly, 123 (2016), 482-485.

Formula

a(n) = A003173(n) = -A048981(6-n) for n = 1, 2, 3, 4, 5.

Crossrefs

Cf. A003173, A003174, A048981.

Sequence in context: A117733 A066236 A118203 * A345742 A064956 A348745

Adjacent sequences: A263462 A263463 A263464 * A263466 A263467 A263468

Keyword

nonn,fini,full

Author

Jonathan Sondow, Oct 19 2015

Status

approved