A094613 -id:A094613 - cp's OEIS frontend

A094612 Fundamental discriminants of real quadratic number fields with class number 3.

229, 257, 316, 321, 469, 473, 568, 733, 761, 892, 993, 1016, 1101, 1229, 1257, 1304, 1373, 1436, 1489, 1509, 1772, 1901, 1929, 1957, 2021, 2089, 2101, 2177, 2213, 2429, 2557, 2589, 2636, 2677, 2713, 2777, 2857, 2917, 2981, 3173, 3221, 3229, 3261, 3356, 3569

Offset: 1

Eric W. Weisstein, May 14 2004

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Class Number
Index entries for sequences related to quadratic fields

Cf. A003656, A094619, A094613-A094614, A218156-A218160.

Select[Range[3569], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 3 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

{ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==3};
for(n=1, 3600, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019

is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 3;
A094612 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
A094612(3700) # G. C. Greubel, Mar 01 2019

Edited by N. J. A. Sloane, May 01 2010

A094614 Fundamental discriminants of real quadratic number fields with class number 5.

Original entry on oeis.org

401, 817, 1093, 1393, 1429, 1641, 1756, 1897, 1996, 2081, 2153, 2908, 3121, 3181, 3253, 3928, 3997, 4353, 4357, 4441, 4504, 4757, 4889, 5241, 5269, 5308, 5944, 6113, 6157, 6481, 6949, 7064, 7229, 7513, 7817, 7861, 8049, 8108, 8121, 8309, 8501, 8689, 9181, 9229

Offset: 1

Eric W. Weisstein, May 14 2004

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Class Number
Index entries for sequences related to quadratic fields

Cf. A003656, A094619, A094612-A094613, A218156-A218160.

Select[Range[9229], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 5 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

{ok(n) = n>10 && isfundamental(n) && qfbclassno(n)==5};
for(n=1, 10000, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019

is_fund_and_qfbcn_1 = lambda n: is_fundamental_discriminant(n) and QuadraticField(n, 'a').class_number() == 5;
A094614 = lambda n: filter(is_fund_and_qfbcn_1, (1, 2, .., n));
A094614(10000) # G. C. Greubel, Mar 01 2019

A081363 Smallest squarefree integer k such that Q(sqrt(k)) has class number n.

Original entry on oeis.org

2, 10, 79, 82, 401, 235, 577, 226, 1129, 1111, 1297, 730, 4759, 1534, 9871, 2305, 7054, 4954, 15409, 3601, 7057, 4762, 23593, 9634, 24859, 13321, 8761, 5626, 49281, 11665, 97753, 15130, 55339, 19882, 25601, 18226, 24337, 19834, 41614, 16899, 55966, 47959

Offset: 1

Dean Hickerson, Mar 19 2003

nonn

What is known about the asymptotics of this sequence? - Charles R Greathouse IV, Jan 26 2017

Records: 2, 10, 79, 82, 401, 577, 1129, 1297, 4759, 9871, 15409, 23593, 24859, 49281, 97753, 106537, 159199, 197137, 212137, 239119, 245023, 444089, 589822, 614849, 815413, 837929, 943951, 1025494, 1224121, 1240369, 1333255, 1334026, ..., . - Robert G. Wilson v, Apr 12 2017

Robert G. Wilson v, Table of n, a(n) for n = 1..214

Cf. A081319, A081364, A094619, A094612, A094613, A094614.

Cf. A219361, A029702, A029703, A029704, A029705, A218038, A218039, A218040, A218041, A218042, A276541. - Robert G. Wilson v, Apr 12 2017

t[] := 0; k = 2; While[k < 56000, cn = NumberFieldClassNumber@Sqrt@k; If[ t[cn] == 0, t[cn] = k; Print[{cn, k}]]; k++]; t@# & /@ Range@ 42 (* _Robert G. Wilson v, Apr 12 2017 *)

v=vector(100); for(n=2,1e6, if(!issquarefree(n), next); t=qfbclassno(if(n%4>1,4*n,n)); if(t<=#v && v[t]==0, v[t]=n; print("a("t") = "n))) \\ Charles R Greathouse IV, Jan 26 2017

More terms from Max Alekseyev, Apr 28 2010

cp's OEIS Frontend

A094612 Fundamental discriminants of real quadratic number fields with class number 3.

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A094614 Fundamental discriminants of real quadratic number fields with class number 5.

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Sage

A081363 Smallest squarefree integer k such that Q(sqrt(k)) has class number n.

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