A006557 Minimal absolute value of discriminants of number fields of degree n. (Formerly M3099)

1, 3, 23, 117, 1609, 9747, 184607, 1257728

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..8.

LMFDB, Number fields

A. M. Odlyzko, Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: A survey of recent results, Sem. Theorie des Nombres, Bordeaux, 2 (1990), pp. 119-141.

Index entries for sequences related to quadratic fields

Formula

a(n) = Min_{A343690(n), A343772(n)}. - Jianing Song, Apr 26 2021

Example

From Jianing Song, Apr 26 2021: (Start)
The number field F of degree n whose discriminant is of minimal absolute value:
n = 2, F = Q[x]/(x^2 - x + 1), d = -3;
n = 3, F = Q[x]/(x^3 - x^2 + 1), d = -23;
n = 4, F = Q[x]/(x^4 - x^3 - x^2 + x + 1), d = 117;
n = 5, F = Q[x]/(x^5 - x^3 - x^2 + x + 1), d = 1609;
n = 6, F = Q[x]/(x^6 - x^5 + x^4 - 2x^3 + 4x^2 - 3x + 1), d = -9747;
n = 7, F = Q[x]/(x^7 - x^6 - x^5 + x^4 - x^2 + x + 1), d = -184607;
n = 8, F = Q[x]/(x^8 - 2x^7 + 4x^5 - 4x^4 + 3x^2 - 2x + 1), d = 1257728. (End)

Crossrefs

Cf. A343690 (the positive discriminant case), A343772 (the negative discriminant case).

Sequence in context: A269235 A245752 A290367 * A362158 A226611 A081628

Adjacent sequences: A006554 A006555 A006556 * A006558 A006559 A006560

Keyword

nonn,hard,more

Author

N. J. A. Sloane.

Extensions

New name by Jianing Song, Apr 26 2021

Status

approved