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.

Showing 1-10 of 20 results. Next

A176026 Bisection of A046125.

Original entry on oeis.org

18, 54, 51, 131, 87, 206, 95, 322, 150, 350, 139, 511, 190, 457, 255, 708, 219, 668, 237, 912, 339, 691, 268, 1365, 345, 770, 427, 1205, 291, 1302, 323, 1672, 530, 976, 560, 1930, 407, 1075, 561, 2277, 402, 1715, 472, 1905, 801, 1248, 509, 3283, 580, 1736
Offset: 1

Views

Author

Michael Ruxton (mruxton(AT)ns.sympatico.ca), Apr 06 2010

Keywords

Crossrefs

Extensions

More terms from Amiram Eldar, May 10 2024

A351664 Discriminants of imaginary quadratic fields with class number 26 (negated).

Original entry on oeis.org

551, 951, 1247, 1256, 1735, 1832, 2651, 2771, 2792, 2823, 2839, 2984, 3092, 3327, 3368, 3611, 3736, 3903, 3992, 4052, 4207, 4244, 4376, 4739, 5123, 5435, 5524, 5891, 6059, 6443, 6515, 6587, 6676, 6847, 6891, 6964, 7156, 8003, 8339, 8383, 8408, 8691, 8743
Offset: 1

Views

Author

Andy Huchala, Feb 16 2022

Keywords

Comments

Sequence contains 190 terms; largest is 103027.
The class group of Q[sqrt(-d)] is isomorphic to C_26 for all d in this sequence.

Crossrefs

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] == 26]

A038552 Largest squarefree number k such that Q(sqrt(-k)) has class number n.

Original entry on oeis.org

163, 427, 907, 1555, 2683, 3763, 5923, 6307, 10627, 13843, 15667, 17803, 20563, 30067, 34483, 31243, 37123, 48427, 38707, 58507, 61483, 85507, 90787, 111763, 93307, 103027, 103387, 126043, 166147, 134467, 133387, 164803, 222643, 189883
Offset: 1

Views

Author

Robert Brewer (rbrewerjr(AT)aol.com)

Keywords

Comments

Conjecture: this is also the largest absolute value of negative fundamental discriminant d for class number n. This is to say, for even n, let k be the largest odd number such that h(-k) = n (if it exists), k' be the largest even number such that h(-k') = n (if it exists), then k > k'; here h(D) is the class number of the quadratic field with discriminant D. [Comment rewritten by Jianing Song, Oct 03 2022]
Numbers so far are all 19 mod 24. - Ralf Stephan, Jul 07 2003

Crossrefs

Programs

  • Mathematica
    << NumberTheory`NumberTheoryFunctions`; a = Table[0, {32} ]; Do[ If[ Mod[n, 4] != 1 || Mod[n, 4] != 2 || SquareFreeQ[n], c = ClassNumber[ -n]; If[c < 33, a[[c]] = n]], {n, 0, 250000} ]; a
  • PARI
    lista() = {my(nn=10^7, NMAX=100, v = vector(NMAX), c); for (k=1, nn, if (isfundamental(-k), if ((c = qfbclassno(-k)) <= NMAX, v[c]=k););); v;} \\ Michel Marcus, Feb 17 2022; takes several minutes

Extensions

More terms from Robert G. Wilson v, Nov 08 2001
2 more terms from Dean Hickerson, May 20 2003. The values were obtained by transcribing and combining data from Tables 1-3 of Buell's paper, which has information for all values of n up to 125.
Values checked against Watkins' data, which proves the values of a(n) for n = 1..100. Charles R Greathouse IV, Feb 08 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.

Crossrefs

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]

A081319 Smallest squarefree integer k such that Q(sqrt(-k)) has class number n, or 0 if no such k exists.

Original entry on oeis.org

1, 5, 23, 14, 47, 26, 71, 41, 199, 74, 167, 89, 191, 101, 239, 146, 383, 293, 311, 194, 431, 269, 647, 329, 479, 314, 983, 341, 887, 461, 719, 446, 839, 614, 1031, 626, 1487, 1199, 1439, 689, 1151, 794, 1847, 854, 1319, 941, 3023, 1106, 1511, 1109, 1559
Offset: 1

Views

Author

Dean Hickerson, Mar 18 2003

Keywords

Examples

			From _Jianing Song_, May 08 2021: (Start)
a(6) = min{A060649(6), A344072(3)/4} = min{87, 104/4} = 26.
a(12) = min{A060649(12), A344072(6)/4} = min{231, 356/4} = 89.
a(18) = min{A060649(12), A344072(9)/4} = min{335, 1172/4} = 293.
a(38) = min{A060649(38), A344072(19)/4} = min{1199, 4916/4} = 1199. (End)
		

Crossrefs

Programs

Formula

a(n) = A060649(n) for odd n > 1. For even n, assuming that A060649(n) > 0 and A344072(n/2) > 0, a(n) = min{A060649(n), A344072(n/2)/4}. - Jianing Song, May 08 2021

Extensions

Edited by Max Alekseyev, Apr 28 2010
Escape clause added by Jianing Song, May 08 2021

A048925 Discriminants of imaginary quadratic fields with class number 24 (negated).

Original entry on oeis.org

695, 759, 1191, 1316, 1351, 1407, 1615, 1704, 1736, 1743, 1988, 2168, 2184, 2219, 2372, 2408, 2479, 2660, 2696, 2820, 2824, 2852, 2856, 2915, 2964, 3059, 3064, 3127, 3128, 3444, 3540, 3560, 3604, 3620, 3720, 3864, 3876, 3891, 3899, 3912
Offset: 0

Views

Author

Keywords

Crossrefs

Programs

  • Mathematica
    Reap[ For[n = 1, n < 4000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 24, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)
  • 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] == 24] # Andy Huchala, Feb 15 2022

A351666 Discriminants of imaginary quadratic fields with class number 28 (negated).

Original entry on oeis.org

831, 935, 1095, 1311, 1335, 1364, 1455, 1479, 1496, 1623, 1703, 1711, 1855, 1976, 2024, 2055, 2120, 2127, 2324, 2359, 2431, 2455, 2564, 2607, 2616, 2703, 3224, 3272, 3396, 3419, 3487, 3535, 3572, 3576, 3608, 3624, 3731, 3848, 3995, 4040, 4183, 4279, 4344
Offset: 1

Views

Author

Andy Huchala, Feb 16 2022

Keywords

Comments

Sequence contains 457 terms; largest is 126043.
The class groups associated to 174 of the above discriminants are isomorphic to C_28, and the remaining 283 have a class group isomorphic to C_14 X C_2.

Crossrefs

Programs

  • PARI
    isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 28}; \\ Michel Marcus, Mar 02 2022
  • 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] == 28]
    

A351679 Discriminants of imaginary quadratic fields with class number 41 (negated).

Original entry on oeis.org

1151, 2551, 2719, 3079, 3319, 3511, 6143, 9319, 9467, 10499, 10903, 11047, 11483, 11719, 11987, 12227, 12611, 13567, 14051, 14411, 14887, 14983, 16067, 16187, 19763, 20407, 20771, 21487, 22651, 24971, 25171, 26891, 26987, 27739, 28547, 29059, 29251, 30859
Offset: 1

Views

Author

Andy Huchala, Mar 28 2022

Keywords

Comments

Sequence contains 109 terms; largest is 296587.
The class group of Q[sqrt(-d)] is isomorphic to C_41 for all d in this sequence.

Crossrefs

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] == 41]

A351665 Discriminants of imaginary quadratic fields with class number 27 (negated).

Original entry on oeis.org

983, 1231, 1399, 1607, 1759, 1879, 1999, 3271, 3299, 3943, 4903, 6007, 6011, 7699, 8867, 10531, 10939, 11003, 11027, 11383, 11491, 11779, 11939, 13411, 14243, 14723, 15107, 15739, 16411, 16547, 17443, 17627, 17659, 17747, 18587, 18787, 18859, 19051, 19427
Offset: 1

Views

Author

Andy Huchala, Feb 16 2022

Keywords

Comments

Sequence contains 93 terms; largest is 103387.
The class group of Q[sqrt(-d)] is isomorphic to C_9 X C_3 for d = 3299, 19427, 34603, 89923, and 98443. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_27.

Crossrefs

Programs

  • PARI
    isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 27}; \\ Michel Marcus, Mar 02 2022
  • 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] == 27]
    

A351667 Discriminants of imaginary quadratic fields with class number 29 (negated).

Original entry on oeis.org

887, 2287, 2311, 2383, 2939, 3583, 3659, 3823, 4451, 4519, 5051, 5743, 6947, 7207, 7643, 7687, 8863, 8963, 9323, 12323, 13763, 13883, 14387, 15139, 15227, 15443, 15467, 15859, 16427, 17491, 20483, 20507, 22051, 23059, 23251, 24859, 25523, 28403, 29587, 29723
Offset: 1

Views

Author

Andy Huchala, Mar 24 2022

Keywords

Comments

Sequence contains 83 terms; largest is 166147.
The class group of Q[sqrt(-d)] is isomorphic to C_29 for all d in this sequence.

Crossrefs

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] == 29]
Showing 1-10 of 20 results. Next