A046015 -id:A046015

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A056987

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

+10
20

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

Jianing Song, Table of n, a(n) for n = 1..95

Eric Weisstein's World of Mathematics, Class Number.

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 *)

CROSSREFS

Cf. A014602, A014603, A006203, A013658, A046002, A046003, A046004, A046005, A046006, A046007, A046008, A046009, A046010, A046011, A046012, A046013, A046014, A046015, A046016, A123563, A046018, A171724, A046020, A048925.

KEYWORD

nonn,fini,full,changed

AUTHOR

Eric W. Weisstein

STATUS

approved

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).

+10
14

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,15

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

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

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]

PROG

(PARI) a(n)=if(isfundamental(-n), qfbclassno(-n), 0) \\ Charles R Greathouse IV, Nov 20 2012

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.

Cf. A003657, A191408.

KEYWORD

easy,nonn,changed

AUTHOR

Robert G. Wilson v, Jun 01 2011

STATUS

approved

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