A051962 -id:A051962 - cp's OEIS frontend

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

N. J. A. Sloane, Jan 04 2000

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

Gilles Lachaud, On real quadratic fields, Bull. Amer. Math. Soc., 17:2 (1987), 307-311.
R. A. Mollin, Quadratics, CRC Press, 1996, Appendix A.

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)

Cf. A050950-A050969, A051962-A051965.

A050969 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.

Original entry on oeis.org

151, 199, 367, 622, 863, 1151, 1454, 1501, 1502, 1941, 2033, 3902, 4101, 4317, 4677, 4821, 5549, 6077, 7277, 8133, 8453, 8813, 9253, 9357, 11381, 11733, 14237, 15837, 17933, 18293, 21653, 23453, 25157, 36077, 49013

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A051965 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 24.

Original entry on oeis.org

271, 382, 607, 753, 911, 1103, 1262, 1438, 1473, 1838, 1982, 2063, 2078, 2558, 2661, 2687, 2893, 2903, 3986, 3113, 3167, 3377, 3669, 4237, 4333, 4533, 5293, 5533, 5753, 6509, 6621, 7197, 7269, 8153, 8189, 8213, 8413, 10637, 11157, 11573, 11589, 11893, 12677, 12797, 13453, 13541, 14117, 15693, 15917, 17133, 17309, 18677, 18933, 19797, 20053, 20373, 20837, 22757, 25709, 25973, 26213, 27317, 34997, 39077

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

a(40) and following from Georg Fischer, Sep 20 2021

A050960 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 11.

Original entry on oeis.org

541, 593, 661, 701, 857, 1061, 1109, 1217, 1237, 1709, 1733, 1949, 2333, 2957, 3677, 3701, 4373, 5237, 5309, 7013, 8693, 9533, 10853, 12437

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A050952 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 3.

Original entry on oeis.org

17, 37, 61, 101, 197, 317, 461, 557, 677, 773, 1877

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A050954 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 5.

Original entry on oeis.org

41, 149, 157, 181, 269, 397, 941, 1013, 2477, 2693, 3533, 4253

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A050951 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 2.

Original entry on oeis.org

3, 6, 11, 21, 38, 77, 83, 93, 227, 237, 437, 453, 1133, 1253

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A050953 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 4.

Original entry on oeis.org

7, 14, 23, 33, 47, 62, 69, 133, 141, 167, 213, 398, 413, 573, 717, 1077, 1293, 1397, 1757, 3053

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A050955 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 6.

Original entry on oeis.org

19, 22, 57, 59, 107, 131, 253, 278, 309, 341, 381, 749, 813, 893, 1893, 2453, 2757, 3317

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

A050956 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 7.

Original entry on oeis.org

89, 109, 113, 137, 373, 389, 509, 653, 797, 853, 997, 1493, 1997, 2309, 2621, 3797, 4973

Offset: 1

N. J. A. Sloane, Jan 04 2000

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

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)

Cf. A050950-A050969, A051962-A051965.

cp's OEIS Frontend

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

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A050969 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.

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A051965 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 24.

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A050960 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 11.

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A050952 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 3.

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A050954 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 5.

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A050951 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 2.

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A050953 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 4.

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A050955 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 6.

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A050956 Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 7.

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