A191410 -id:A191410 - cp's OEIS frontend

A046007 Discriminants of imaginary quadratic fields with class number 10 (negated).

119, 143, 159, 296, 303, 319, 344, 415, 488, 611, 635, 664, 699, 724, 779, 788, 803, 851, 872, 916, 923, 1115, 1268, 1384, 1492, 1576, 1643, 1684, 1688, 1707, 1779, 1819, 1835, 1891, 1923, 2152, 2164, 2363, 2452, 2643, 2776, 2836, 2899, 3028

Offset: 1

Eric W. Weisstein

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

Andrew Howroyd, Table of n, a(n) for n = 1..87
Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

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

Cf. A191410.

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[14000], NumberFieldClassNumber[Sqrt[-#]] == 10 &]] (* Jean-François Alcover, Jun 27 2012 *)

ok(n)={isfundamental(-n) && qfbclassno(-n) == 10} \\ Andrew Howroyd, Jul 24 2018

[n for n in (1..3500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==10] # G. C. Greubel, Mar 01 2019

A046009 Discriminants of imaginary quadratic fields with class number 12 (negated).

Original entry on oeis.org

231, 255, 327, 356, 440, 516, 543, 655, 680, 687, 696, 728, 731, 744, 755, 804, 888, 932, 948, 964, 984, 996, 1011, 1067, 1096, 1144, 1208, 1235, 1236, 1255, 1272, 1336, 1355, 1371, 1419, 1464, 1480, 1491, 1515, 1547, 1572, 1668, 1720, 1732

Offset: 1

Eric W. Weisstein

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

Andrew Howroyd, Table of n, a(n) for n = 1..206
Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330
Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
Eric Weisstein's World of Mathematics, Class Number.
Index entries for sequences related to quadratic fields

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

Cf. A191410.

Reap[ For[n = 1, n < 2000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 12, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

ok(n)={isfundamental(-n) && qfbclassno(-n) == 12} \\ Andrew Howroyd, Jul 24 2018

[n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==12] # G. C. Greubel, Mar 01 2019

A191411 Class number, k, of n; i.e., imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not squarefree (A005117).

Original entry on oeis.org

1, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 2, 4, 2, 0, 4, 0, 1, 0, 4, 2, 3, 0, 0, 6, 0, 0, 6, 4, 3, 0, 4, 4, 2, 0, 2, 6, 4, 0, 8, 4, 1, 0, 0, 4, 5, 0, 0, 0, 2, 0, 6, 0, 4, 0, 4, 2, 3, 0, 6, 8, 0, 0, 8, 8, 1, 0, 8, 4, 7, 0, 4, 10, 0, 0, 8, 4, 5, 0, 0, 4, 3, 0, 4, 10, 6, 0, 12, 0, 2, 0, 4, 8, 8, 0, 4, 0, 0, 0, 14, 4, 5, 0, 8

Offset: 1

Robert G. Wilson v, Jun 01 2011

Eric Weisstein's World of Mathematics, Class Number
Index entries for sequences related to quadratic fields

a(n)= 0: A013929; a(n)= 1: A003173; a(n)= 2: A005847; a(n)= 3: A006203; a(n)= 4: A046085; a(n)= 5: A046002; a(n)= 6: A055109; a(n)= 7: A046004; a(n)= 8: A055110; a(n)= 9: A046006; a(n)=10: A055111; a(n)=11: A046008; a(n)=12: n/a;
a(n)=13: A046010; a(n)=14: n/a; a(n)=15: A046012; a(n)=16: n/a; a(n)=17: A046014; a(n)=18: n/a; a(n)=19: A046016;
a(n)=20: n/a; a(n)=21: A046018; a(n)=22: n/a;
a(n)=23: A046020; a(n)=24: n/a; a(n)=25: A056987; etc.
Cf. A191408, A191410.
Cf. A000924 (without the zeros).

f[n_] := If[! SquareFreeQ@ n, 0, NumberFieldClassNumber@Sqrt@ -n]; Array[f, 105]

a(n) = if (! issquarefree(n), 0, qfbclassno(-n*if((-n)%4>1, 4, 1))); \\ Michel Marcus, Jul 08 2015

cp's OEIS Frontend

A046007 Discriminants of imaginary quadratic fields with class number 10 (negated).

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A046009 Discriminants of imaginary quadratic fields with class number 12 (negated).

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

A191411 Class number, k, of n; i.e., imaginary quadratic fields negated Q(sqrt(-n))=k, or 0 if n is not squarefree (A005117).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI