A244338 Decimal expansion of the upper bound of the 6-dimensional simultaneous Diophantine approximation constant.

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

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..99.

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

Eric Weisstein's MathWorld, Blichfeldt's Theorem

Formula

Equals 1/(k*2^(k+1)*integral_(0..1) x^(k-1)/((x^k+1)*(x+1)^k) dx, with k = 5.

Equals 1/(32 - (64*sqrt(50 - 82/sqrt(5))*Pi)/25). - Jean-François Alcover, Aug 11 2021

Example

0.3790226044011379423944841026...

Mathematica

1/(k*2^(k+1)*Integrate[x^(k-1)/((x^k+1)*(x+1)^k), {x, 0, 1}]) /. k -> 5 // Re // N[#, 100]& // RealDigits // First

Crossrefs

Cf. A244334, A244335, A244336, A244337.

Sequence in context: A118622 A101366 A217359 * A336045 A090458 A131712

Adjacent sequences: A244335 A244336 A244337 * A244339 A244340 A244341

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 26 2014

Status

approved