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A174198 Floor of inverse of Minkowski's constant. 1
0, 1, 3, 8, 20, 50, 128, 326, 838, 2164, 5613, 14619, 38200, 100109, 263002, 692452, 1826640, 4826740, 12773610, 33850507, 89815472, 238573535, 634359840, 1688317073, 4497222961, 11988860360, 31983701435, 85383496739, 228083043888 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The subsequence of primes begins: 3, 100109. As a final application of Minkowski's theorem, Stevenhagen shows that the unit group of an order R in a number field with r real and 2s complex embeddings is finitely generated of free rank r + s - 1 (Dirichlet unit theorem).
LINKS
P. Stevenhagen, Number Rings, Chapter 5, Geometry of numbers.
FORMULA
a(n) = floor((n^n)*Pi/(4*n!)) = floor((Pi/4)*A000312(n)/A000142(n)).
EXAMPLE
a(0) = floor((1^1)*Pi/(4*1!)) = floor(0.78539816339744830962) = 0.
a(10) = floor((10^10)*Pi/(4*10!)) = floor(2164.3467906675714) = 2164.
MAPLE
Digits := 200 : A174198 := proc(n) n^n*Pi/4/n! ; floor(%) ; end proc: seq(A174198(n), n=1..30) ; # R. J. Mathar, Apr 15 2010
CROSSREFS
Sequence in context: A187003 A101893 A140662 * A077997 A294407 A295346
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 11 2010
EXTENSIONS
More terms from R. J. Mathar, Apr 15 2010
STATUS
approved

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Last modified June 20 02:43 EDT 2024. Contains 373512 sequences. (Running on oeis4.)