A174198 Floor of inverse of Minkowski's constant.

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

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

Table of n, a(n) for n=1..29.

P. Stevenhagen, Number Rings, Chapter 5, Geometry of numbers.

Minkowski's Constant, at Planet Math.

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

Cf. A000142, A000312.

Sequence in context: A187003 A101893 A140662 * A077997 A294407 A295346

Adjacent sequences: A174195 A174196 A174197 * A174199 A174200 A174201

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 11 2010

Extensions

More terms from R. J. Mathar, Apr 15 2010

Status

approved