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A261813
Decimal expansion of (Pi/4)^N*(N^N/N!)^2 for N = 3.
1
9, 8, 1, 0, 5, 7, 9, 7, 3, 0, 8, 7, 6, 1, 1, 4, 9, 7, 7, 3, 9, 6, 8, 0, 2, 8, 1, 4, 2, 0, 0, 0, 5, 0, 8, 2, 5, 7, 0, 4, 0, 9, 5, 2, 1, 0, 2, 9, 9, 5, 8, 4, 8, 5, 6, 3, 5, 0, 4, 2, 0, 2, 5, 9, 4, 0, 7, 4, 9, 2, 1, 4, 1, 8, 5, 4, 3, 8, 3, 5, 5, 0, 9, 4, 8, 8, 3, 8, 9, 9, 8, 5, 9, 7, 0, 0, 6, 9, 5, 9, 5, 1, 3, 4, 3
OFFSET
1,1
COMMENTS
The general expression is a lower bound (due to H. Minkowski) on the discriminant of a number field of degree N.
The corresponding value for N = 2 matches A091476.
REFERENCES
B. Mazur, Algebraic Numbers, in The Princeton Companion to Mathematics, Editor T. Gowers, Princeton University Press, 2008, Section IV.1, page 330.
LINKS
FORMULA
Equals 81*Pi^3/256.
EXAMPLE
9.8105797308761149773968028142000508257040952102995848563504202594...
MATHEMATICA
n = 3; First@ RealDigits[N[(Pi/4)^n (n^n/n!)^2, 120]] (* Michael De Vlieger, Nov 19 2015 *)
PROG
(PARI) N=3; (Pi/4)^N*(N^N/N!)^2
CROSSREFS
Cf. A000796, A091476 (N=2).
Sequence in context: A232737 A155683 A343469 * A373863 A198920 A354593
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Nov 19 2015
STATUS
approved