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A006557
Minimal absolute value of discriminants of number fields of degree n.
(Formerly M3099)
3
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).
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
KEYWORD
nonn,hard,more
AUTHOR
EXTENSIONS
New name by Jianing Song, Apr 26 2021
STATUS
approved

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