A029704 -id:A029704 - cp's OEIS frontend

A029705 Squarefree n such that Q(sqrt(n)) has class number 5.

401, 439, 499, 727, 817, 982, 1093, 1126, 1327, 1393, 1429, 1486, 1641, 1766, 1897, 2027, 2081, 2153, 2399, 2878, 3121, 3134, 3181, 3238, 3251, 3253, 3814, 3967, 3997, 4271, 4353, 4357, 4358, 4441, 4591, 4622, 4757, 4889, 5107, 5241, 5269, 5527, 5711, 5774

Offset: 1

Paolo Dominici (pl.dm(AT)libero.it)

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to quadratic fields

Cf. A003172, A029702-A029704, A218038-A218042.

Select[Range[5774], SquareFreeQ[#] && NumberFieldClassNumber@Sqrt[#] == 5 &] (* Arkadiusz Wesolowski, Oct 22 2012 *)

is(n)=issquarefree(n)&&bnfinit('x^2-n).cyc==[5] \\ Charles R Greathouse IV, Oct 18 2012

A029703 Q(sqrt(n)) has class number 3.

Original entry on oeis.org

79, 142, 223, 229, 254, 257, 321, 326, 359, 443, 469, 473, 659, 733, 761, 839, 934, 993, 1091, 1101, 1171, 1223, 1229, 1257, 1367, 1373, 1478, 1489, 1509, 1523, 1567, 1627, 1646, 1787, 1811, 1847, 1901, 1907, 1929, 1957, 1987, 2021, 2089, 2099, 2101, 2143, 2177, 2207, 2213

Offset: 1

Paolo Dominici (pl.dm(AT)libero.it)

nonn

			79 is in the sequence because Z[sqrt(79)] has class number 3.
Z[sqrt(82)] has class number 4 and therefore 82 is not in the sequence.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to quadratic fields

Cf. A003172, A029702, A029704-A029705, A218038-A218042.

Select[Range[2000], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 3 &] (* Alonso del Arte, Oct 17 2012 *)

A007947(n)={my(p); p=factor(n)[, 1]; prod(i=1, length(p), p[i]); }
{ for (n=2, 10^4,
    if ( n!=A007947(n), next() );
    K = bnfinit(x^2 - n);
    if ( K.cyc == [3], print1( n, ", ") );
); }
/* Joerg Arndt, Oct 18 2012 */

Missing initial term (79) added by Alonso del Arte, Oct 17 2012

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

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A029705 Squarefree n such that Q(sqrt(n)) has class number 5.

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A029703 Q(sqrt(n)) has class number 3.

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

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