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.

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A037449 Discriminant of quadratic field Q(sqrt(n)).

Original entry on oeis.org

1, 8, 12, 1, 5, 24, 28, 8, 1, 40, 44, 12, 13, 56, 60, 1, 17, 8, 76, 5, 21, 88, 92, 24, 1, 104, 12, 28, 29, 120, 124, 8, 33, 136, 140, 1, 37, 152, 156, 40, 41, 168, 172, 44, 5, 184, 188, 12, 1, 8, 204, 13, 53, 24, 220, 56, 57, 232, 236, 60, 61, 248, 28, 1, 65, 264, 268, 17, 69
Offset: 1

Views

Author

Jason Earls, Jun 30 2001

Keywords

Comments

For the discriminant of the quadratic field Q(sqrt(-n)), see A204993.
a(n) is the smallest positive N such that (n/k) = (n/(k mod N)) for every odd k that is coprime to n, where (n/k) is the Jacobi symbol. As we have Dirichlet's theorem on arithmetic progressions, a(n) is also the smallest positive N such that (n/p) = (n/(p mod N)) for every odd prime p that is not a factor of n. - Jianing Song, May 16 2024

Links

Crossrefs

Cf. A204993, A007913.

Programs

  • Mathematica
    Table[NumberFieldDiscriminant[Sqrt[n]], {n, 100}] (* Artur Jasinski, Jan 27 2012 *)
  • PARI
    vector(150,n,quaddisc(n))
  • Sage
    [fundamental_discriminant(n) for n in (1..69)] # Peter Luschny, Oct 15 2018

Formula

Let b(n) = A007913(n), then a(n) = b(n) if b(n) == 1 (mod 4) and 4*b(n) otherwise. - Jianing Song, May 16 2024

A236546 Discriminant of A048981(n) (= squarefree integers for which the quadratic field Q[sqrt(D)] is norm-Euclidean).

Original entry on oeis.org

-11, -7, -3, -8, -4, 8, 12, 5, 24, 28, 44, 13, 17, 76, 21, 29, 33, 37, 41, 57, 73
Offset: 1

Views

Author

M. F. Hasler, Jan 28 2014

Keywords

Comments

Note that here, values are not sorted by size, but in direct correspondence with terms of A048981. This is in contrast to A003246, where the same positive values are listed by size.

Crossrefs

Cf. A003174, A003246, A037449, A048981, A204993, A187776.

Programs

Formula

a(n) = A037449(A048981(n)) for n>5, a(n) = -A204993(-A048981(n)) for n <= 5.
Showing 1-2 of 2 results.

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