A050950 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 1.

2, 5, 13, 29, 53, 173, 293

Offset

1,1

Comments

Theorem 3.1 of Lachaud (1987) says that under Hypothesis(H), which is a version of the Generalized Riemann Hypothesis, the only real quadratic fields with caliber one are the fields Q(sqrt(t)) where t is one of the seven numbers listed here. - N. J. A. Sloane, Aug 28 2021

References

Gilles Lachaud, On real quadratic fields, Bull. Amer. Math. Soc., 17:2 (1987), 307-311.

R. A. Mollin, Quadratics, CRC Press, 1996, Appendix A.

Links

Table of n, a(n) for n=1..7.

R. A. Mollin and H. C. Williams, On a determination of real quadratic fields of class number one and related continued fraction period length less than 25, Proc. Japan Acad. Ser. A Math. Sci. Volume 67, Number 1 (1991), 20-25. (cf. Table 3.1)

Crossrefs

Cf. A050950-A050969, A051962-A051965.

Sequence in context: A158708 A093702 A011756 * A259678 A218152 A079991

Adjacent sequences: A050947 A050948 A050949 * A050951 A050952 A050953

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Jan 04 2000

Status

approved