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A244338 Decimal expansion of the upper bound of the 6-dimensional simultaneous Diophantine approximation constant. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.23 Diophantine Approximation Constants, p. 174.
LINKS
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
Sequence in context: A118622 A101366 A217359 * A336045 A090458 A131712
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified July 25 04:49 EDT 2024. Contains 374586 sequences. (Running on oeis4.)