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 1-4 of 4 results.

A013658 Discriminants of imaginary quadratic fields with class number 4 (negated).

Original entry on oeis.org

39, 55, 56, 68, 84, 120, 132, 136, 155, 168, 184, 195, 203, 219, 228, 259, 280, 291, 292, 312, 323, 328, 340, 355, 372, 388, 408, 435, 483, 520, 532, 555, 568, 595, 627, 667, 708, 715, 723, 760, 763, 772, 795, 955, 1003, 1012, 1027, 1227, 1243, 1387, 1411, 1435, 1507, 1555
Offset: 1

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Author

Eric Rains (rains(AT)caltech.edu)

Keywords

References

  • H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, p. 229.

Crossrefs

Programs

  • Mathematica
    Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[1250], NumberFieldClassNumber[Sqrt[-#]] == 4 &]] (* Jean-François Alcover, Jun 27 2012 *)
  • PARI
    ok(n)={isfundamental(-n) && quadclassunit(-n).no == 4} \\ Andrew Howroyd, Jul 20 2018
    
  • Sage
    [n for n in (1..2000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==4] # G. C. Greubel, Mar 01 2019

Extensions

a(50)-a(54) added by Andrew Howroyd, Jul 20 2018

A056987 Discriminants of imaginary quadratic fields with class number 25 (negated).

Original entry on oeis.org

479, 599, 1367, 2887, 3851, 4787, 5023, 5503, 5843, 7187, 7283, 7307, 7411, 8011, 8179, 9227, 9923, 10099, 11059, 11131, 11243, 11867, 12211, 12379, 12451, 12979, 14011, 14923, 15619, 17483, 18211, 19267, 19699, 19891, 20347, 21107, 21323
Offset: 1

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Author

Keywords

Comments

Sequence contains 95 members; largest is 93307.
The class group of Q[sqrt(-d)] is isomorphic to C_5 X C_5 for d = 12451 and 37363. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_25. - Jianing Song, Dec 01 2019

Crossrefs

Programs

  • Mathematica
    Reap[ For[n = 1, n < 22000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 25, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

A191410 Class number, k, of n, i.e.; imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not a fundamental discriminant (A003657).

Original entry on oeis.org

0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 2, 2, 0, 0, 4, 4, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 3, 4, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 5, 6, 0
Offset: 1

Views

Author

Robert G. Wilson v, Jun 01 2011

Keywords

Crossrefs

a(n)= 0: n/a The complement of A003657; a(n)= 1: A014602; a(n)= 2: A014603; a(n)= 3: A006203; a(n)= 4: A013658; a(n)= 5: A046002; a(n)= 6: A046003; a(n)= 7: A046004; a(n)= 8: A046005; a(n)= 9: A046006; a(n)=10: A046007; a(n)=11: A046008; a(n)=12: A046009; a(n)=13: A046010; a(n)=14: A046011; a(n)=15: A046012; a(n)=16: A046013; a(n)=17: A046014; a(n)=18: A046015; a(n)=19: A046016; a(n)=20: A123563; a(n)=21: A046018; a(n)=22: A171724; a(n)=23: A046020; a(n)=24: A048925; a(n)=25: A056987; etc.

Programs

  • Mathematica
    FundamentalDiscriminantQ[n_] := n != 1 && (Mod[n, 4] == 1 || !Unequal[ Mod[n, 16], 8, 12]) && SquareFreeQ[n/2^IntegerExponent[n, 2]] (* via Eric E. Weisstein *);
    f[n_] := If[ !FundamentalDiscriminantQ@ -n, 0, NumberFieldClassNumber@ Sqrt@ -n]; Array[f, 105]
  • PARI
    a(n)=if(isfundamental(-n),qfbclassno(-n),0) \\ Charles R Greathouse IV, Nov 20 2012

A305416 Negated discriminants of imaginary quadratic number fields whose class group is isomorphic to the Klein 8-group, C_2 x C_2 x C_2.

Original entry on oeis.org

420, 660, 840, 1092, 1155, 1320, 1380, 1428, 1540, 1848, 1995, 3003, 3315
Offset: 1

Views

Author

Vincenzo Librandi, Jun 12 2018

Keywords

Comments

Intersection of A046005 and A003644. Note that A003644 = A014602 union A014603 union A192322 union {a(n)} union {5460}. - Jianing Song, Jul 12 2018

Crossrefs

Subsequence of A046005 and A003644.

Programs

Showing 1-4 of 4 results.