A244337 Decimal expansion of the upper bound of the 5-dimensional simultaneous Diophantine approximation constant.

3, 9, 0, 7, 3, 1, 3, 8, 2, 9, 6, 5, 2, 4, 5, 2, 8, 7, 3, 2, 6, 8, 6, 6, 6, 8, 6, 0, 9, 5, 8, 9, 8, 0, 1, 3, 6, 2, 7, 5, 9, 0, 9, 6, 4, 7, 5, 5, 7, 3, 5, 0, 3, 2, 4, 7, 7, 4, 9, 5, 1, 0, 4, 3, 5, 7, 7, 0, 3, 3, 9, 6, 2, 7, 2, 3, 8, 9, 1, 4, 4, 7, 6, 2, 2, 1, 9, 1, 8, 8, 8, 8, 0, 6, 1, 3, 3, 7, 5, 9, 8, 7, 6

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.23 Diophantine Approximation Constants, p. 174.

Links

Table of n, a(n) for n=0..102.

W. G. Spohn, Blichfeldt's Theorem and Simultaneous Diophantine Approximation

Eric Weisstein's MathWorld, Blichfeldt's Theorem

Formula

1/(k*2^(k+1)*integral_(0..1) x^(k-1)/((x^k+1)*(x+1)^k) dx = 3/(208 + 72*Pi - 96*sqrt(2)*Pi), with k = 4.

Example

0.390731382965245287326866686095898...

Mathematica

RealDigits[3/(208 + 72*Pi - 96*Sqrt[2]*Pi), 10, 103] // First

Crossrefs

Cf. A244334, A244335, A244337, A244338.

Sequence in context: A154540 A324834 A019832 * A338033 A087566 A011337

Adjacent sequences: A244334 A244335 A244336 * A244338 A244339 A244340

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 26 2014

Status

approved