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 1-3 of 3 results.

A046002 Discriminants of imaginary quadratic fields with class number 5 (negated).

Original entry on oeis.org

47, 79, 103, 127, 131, 179, 227, 347, 443, 523, 571, 619, 683, 691, 739, 787, 947, 1051, 1123, 1723, 1747, 1867, 2203, 2347, 2683
Offset: 1

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Author

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Crossrefs

Programs

  • Mathematica
    Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[2700], NumberFieldClassNumber[Sqrt[-#]] == 5 &]] (* Jean-François Alcover, Jun 27 2012 *)
  • PARI
    select(n->qfbclassno(-n)==5,vector(670,n,4*n+3)) \\ Charles R Greathouse IV, Apr 25 2013
    
  • Sage
    [n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==5] # G. C. Greubel, Mar 01 2019

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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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

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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
Showing 1-3 of 3 results.