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.

Previous Showing 11-14 of 14 results.

A218157 Fundamental discriminants of real quadratic number fields with class number 7.

Original entry on oeis.org

577, 1009, 1601, 1761, 2029, 2913, 4229, 4348, 5176, 5273, 5417, 7736, 8097, 8661, 8773, 9004, 9029, 9049, 9101, 9208, 9289, 9868, 10117, 10313, 10357, 10713, 10957, 11021, 11053, 11269, 11537, 11621, 12497, 12977, 13049, 13313, 13701, 14201, 15277, 15809
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 22 2012

Keywords

Links

Crossrefs

Cf. A003656, A094619, A094612-A094614, A218156, A218158-A218160.

Programs

  • Mathematica
    Select[Range[15809], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 7 &]

A218158 Fundamental discriminants of real quadratic number fields with class number 8.

Original entry on oeis.org

904, 1596, 1705, 1768, 1785, 2584, 2605, 2705, 3081, 3196, 3201, 3480, 3640, 3976, 4092, 4161, 4305, 4488, 4620, 4669, 4956, 5160, 5196, 5249, 5305, 5404, 5513, 5713, 5772, 5784, 5865, 6360, 6409, 6565, 6757, 6953, 6972, 7449, 7585, 7656, 7788, 7833, 7980, 8005
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 22 2012

Keywords

Links

Crossrefs

Cf. A003656, A094619, A094612-A094614, A218156-A218157, A218159-A218160.

Programs

  • Mathematica
    Select[Range[8005], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 8 &]

A218159 Fundamental discriminants of real quadratic number fields with class number 9.

Original entry on oeis.org

1129, 3137, 4409, 5521, 6616, 6809, 7573, 7873, 10273, 10721, 11641, 12409, 12657, 13069, 14876, 15629, 16321, 17273, 17989, 18136, 18633, 19441, 21781, 22492, 22497, 23512, 24029, 24169, 24697, 24781, 25361, 26573, 27221, 27349, 28901, 29317, 31897
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 22 2012

Keywords

Links

Crossrefs

Cf. A003656, A094619, A094612-A094614, A218156-A218158, A218160.

Programs

  • Mathematica
    Select[Range[31897], NumberFieldDiscriminant@Sqrt[#] == # && NumberFieldClassNumber@Sqrt[#] == 9 &]

A344409 Positive discriminants of orders with class number 3.

Original entry on oeis.org

148, 229, 257, 316, 321, 404, 469, 473, 564, 568, 592, 621, 733, 756, 761, 788, 837, 892, 916, 993, 1016, 1028, 1076, 1101, 1229, 1257, 1264, 1284, 1304, 1332, 1373, 1396, 1436, 1489, 1492, 1509, 1524, 1556, 1573, 1593, 1616, 1620, 1772, 1876, 1892, 1901, 1929, 1944
Offset: 1

Views

Author

Jianing Song, May 17 2021

Keywords

Comments

Also positive discriminants of orders with class group isomorphic to C_3.
The fundamental terms are listed in A094612.
It seems that for most k in this sequence, 4*k is also in this sequence. The smallest k such that this is not true is k = 564.
Conjecture: if a term k is congruent to 4 modulo 16, then k/4 is either here or in A133315; if a term k is congruent to 0 modulo 16, then k/4 is in this sequence.
Conjecture: a term k is in A006832 if and only if k/4 is not in this sequence.

Links

Crossrefs

Cf. A133315 (positive discriminants of orders with class number 1), A344408 (class number 2), this sequence (class number 3).
Cf. A328825 (the negative discriminant case), A094612, A006832.

Programs

  • PARI
    isA344409(d) = (d>0) && !issquare(d) && ((d%4==0)||(d%4==1)) && quadclassunit(d)[2]==[3]
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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