A244337 - OEIS

%I #12 Nov 09 2024 19:14:30

%S 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,

%T 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,

%U 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

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

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

%H W. G. Spohn, <a href="http://www.jstor.org/discover/10.2307/2373489">Blichfeldt's Theorem and Simultaneous Diophantine Approximation</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BlichfeldtsTheorem.html">Blichfeldt's Theorem</a>

%F Equals 1/(k*2^(k+1)*Integral_{x=0..1} x^(k-1)/((x^k+1)*(x+1)^k) dx), with k = 4.

%F Equals 3/(208 + 72*Pi - 96*sqrt(2)*Pi).

%e 0.390731382965245287326866686095898...

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

%Y Cf. A244334, A244335, A244337, A244338.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Jun 26 2014