cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A046006 Discriminants of imaginary quadratic fields with class number 9 (negated).

Original entry on oeis.org

199, 367, 419, 491, 563, 823, 1087, 1187, 1291, 1423, 1579, 2003, 2803, 3163, 3259, 3307, 3547, 3643, 4027, 4243, 4363, 4483, 4723, 4987, 5443, 6043, 6427, 6763, 6883, 7723, 8563, 8803, 9067, 10627
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

The class group of Q[sqrt(-4027)] is isomorphic to C_3 X C_3. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_9. - Jianing Song, Dec 01 2019

Links

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020.
Cf. A191410.

Programs

  • Mathematica
    Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[10700], NumberFieldClassNumber[Sqrt[-#]] == 9 &]] (* Jean-François Alcover, Jun 27 2012 *)
  • PARI
    ok(n)={isfundamental(-n) && quadclassunit(-n).no == 9};
for(n=1, 11000, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019
  • Sage
    [n for n in (1..4000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==9] # G. C. Greubel, Mar 01 2019

A046018 Discriminants of imaginary quadratic fields with class number 21 (negated).

Original entry on oeis.org

431, 503, 743, 863, 1931, 2503, 2579, 2767, 2819, 3011, 3371, 4283, 4523, 4691, 5011, 5647, 5851, 5867, 6323, 6691, 7907, 8059, 8123, 8171, 8243, 8387, 8627, 8747, 9091, 9187, 9811, 9859, 10067, 10771, 11731, 12107, 12547, 13171, 13291
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

85 discriminants in this sequence (proved).

Links

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002 - A046020.

Programs

  • Mathematica
    Reap[ For[n = 1, n < 14000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 21, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A351680 Discriminants of imaginary quadratic fields with class number 42 (negated).

Original entry on oeis.org

1959, 2183, 2911, 3039, 3176, 3687, 3831, 4039, 4103, 4184, 4735, 4904, 4952, 5288, 5935, 5959, 6179, 6452, 6487, 6611, 6623, 6632, 6836, 7447, 7604, 7811, 7892, 7988, 8459, 8552, 8579, 8744, 8852, 9368, 9428, 9607, 10231, 10643, 10772, 10996, 11023, 11099
Offset: 1

Views

Author

Andy Huchala, Mar 28 2022

Keywords

Comments

Sequence contains 339 terms; largest is 280267.
The class group of Q[sqrt(-d)] is isomorphic to C_42 for all d in this sequence.

Links

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351679.

Programs

  • Sage
    ls = [(QuadraticField(-n, 'a').discriminant(), QuadraticField(-n, 'a').class_number()) for n in (0..10000) if is_fundamental_discriminant(-n) and not is_square(n)];
[-a[0] for a in ls if a[1] == 42]

A046016 Discriminants of imaginary quadratic fields with class number 19 (negated).

Original entry on oeis.org

311, 359, 919, 1063, 1543, 1831, 2099, 2339, 2459, 3343, 3463, 3467, 3607, 4019, 4139, 4327, 5059, 5147, 5527, 5659, 6803, 8419, 8923, 8971, 9619, 10891, 11299, 15091, 15331, 16363, 16747, 17011, 17299, 17539, 17683, 19507, 21187, 21211, 21283, 23203, 24763, 26227, 27043, 29803, 31123, 37507, 38707
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

47 discriminants in this sequence (proved).

Links

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Programs

  • Mathematica
    Reap[ For[ n = 1, n < 40000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 19, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A046085 Numbers n such that Q(sqrt(-n)) has class number 4.

Original entry on oeis.org

14, 17, 21, 30, 33, 34, 39, 42, 46, 55, 57, 70, 73, 78, 82, 85, 93, 97, 102, 130, 133, 142, 155, 177, 190, 193, 195, 203, 219, 253, 259, 291, 323, 355, 435, 483, 555, 595, 627, 667, 715, 723, 763, 795, 955, 1003, 1027, 1227, 1243, 1387, 1411, 1435, 1507, 1555
Offset: 1

Views

Author

N. J. A. Sloane, Jun 16 2000

Keywords

Comments

Contains 54 numbers [Arno, Theorem 7], ..., 1387, 1411, 1435, 1507 and 1555. [R. J. Mathar, May 01 2010]

Links

Crossrefs

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

Programs

A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).

Original entry on oeis.org

95, 111, 164, 183, 248, 260, 264, 276, 295, 299, 308, 371, 376, 395, 420, 452, 456, 548, 552, 564, 579, 580, 583, 616, 632, 651, 660, 712, 820, 840, 852, 868, 904, 915, 939, 952, 979, 987, 995, 1032, 1043, 1060, 1092, 1128, 1131, 1155, 1195, 1204
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

131 discriminants in this sequence (almost certainly but not proved).

Links

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A305416.
Cf. A191410.

Programs

  • Mathematica
    Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[6400], NumberFieldClassNumber[Sqrt[-#]] == 8 &]] (* Jean-François Alcover, Jun 27 2012 *)
  • PARI
    ok(n)={isfundamental(-n) && quadclassunit(-n).no == 8} \\ Andrew Howroyd, Jul 20 2018
  • Sage
    [n for n in (1..6500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==8] # G. C. Greubel, Mar 01 2019

A046012 Discriminants of imaginary quadratic fields with class number 15 (negated).

Original entry on oeis.org

239, 439, 751, 971, 1259, 1327, 1427, 1567, 1619, 2243, 2647, 2699, 2843, 3331, 3571, 3803, 4099, 4219, 5003, 5227, 5323, 5563, 5827, 5987, 6067, 6091, 6211, 6571, 7219, 7459, 7547, 8467, 8707, 8779, 9043, 9907, 10243, 10267, 10459, 10651
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

68 discriminants in this sequence (proved).

Links

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Programs

  • Mathematica
    Reap[ For[n = 1, n < 12000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 15, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A055109 Numbers k such that Q(sqrt(-k)) has class number 6.

Original entry on oeis.org

26, 29, 38, 53, 61, 87, 106, 109, 118, 157, 202, 214, 247, 262, 277, 298, 339, 358, 397, 411, 451, 515, 707, 771, 835, 843, 1059, 1099, 1147, 1203, 1219, 1267, 1315, 1347, 1363, 1563, 1603, 1843, 1915, 1963, 2227, 2283, 2443, 2515, 2563, 2787
Offset: 1

Views

Author

N. J. A. Sloane, Jun 16 2000

Keywords

Links

Crossrefs

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

Programs

  • Mathematica
    Select[Range[10000], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 6 &] (* Jinyuan Wang, Mar 08 2020 *)
  • PARI
    \\  See A005847.

A055110 Numbers k such that Q(sqrt(-k)) has class number 8.

Original entry on oeis.org

41, 62, 65, 66, 69, 77, 94, 95, 105, 111, 113, 114, 137, 138, 141, 145, 154, 158, 165, 178, 183, 205, 210, 213, 217, 226, 238, 258, 265, 273, 282, 295, 299, 301, 310, 313, 322, 330, 337, 345, 357, 371, 382, 385, 395, 418, 438, 442, 445, 457
Offset: 1

Views

Author

N. J. A. Sloane, Jun 16 2000

Keywords

Links

Crossrefs

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

Programs

  • Mathematica
    Select[Range[10000], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 8 &] (* Jinyuan Wang, Mar 08 2020 *)
  • PARI
    \\ See A005847.

A055111 Numbers k such that Q(sqrt(-k)) has class number 10.

Original entry on oeis.org

74, 86, 119, 122, 143, 159, 166, 181, 197, 218, 229, 303, 317, 319, 346, 373, 394, 415, 421, 422, 538, 541, 611, 613, 635, 694, 699, 709, 757, 779, 803, 851, 853, 877, 923, 982, 1093, 1115, 1213, 1318, 1643, 1707, 1779, 1819, 1835, 1891, 1923
Offset: 1

Views

Author

N. J. A. Sloane, Jun 16 2000

Keywords

Links

Crossrefs

See A003173, A005847, A006203, A046085, A046002, A055109, A046004, A055110, A046006, A055111 for class numbers 1 through 10.

Programs

  • Mathematica
    Select[Range[10000], MoebiusMu[#] != 0 && NumberFieldClassNumber[Sqrt[-#]] == 10 &] (* Jinyuan Wang, Mar 08 2020 *)
  • PARI
    \\ See A005847.
Previous Showing 11-20 of 51 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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