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Decimal expansion of the variance associated with the fraction of guests without a napkin in Conway’s napkin problem.
1

%I #14 Jan 17 2020 16:18:25

%S 0,3,4,7,6,3,1,0,5,5,6,1,0,2,6,0,6,5,6,3,3,6,9,7,4,5,4,7,7,9,4,7,0,1,

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

%U 4,0,1,7,1,0,3,6,6,2,4,3,0,3,7,5,2,0,2,4,2,1,2,4,9,1,2,5,6,2,7,3

%N Decimal expansion of the variance associated with the fraction of guests without a napkin in Conway’s napkin problem.

%H Anders Claesson, T. Kyle Petersen, <a href="http://arxiv.org/abs/math/0505080">Conway’s napkin problem</a>, arXiv:math/0505080 [math.CO] 2005.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 2.

%F Equals (3 - e)*(2 - sqrt(e))^2.

%e 0.034763105561026065633697454779470105240123600705...

%t Join[{0}, RealDigits[(3 - E)*(2 - Sqrt[E])^2, 10, 99] // First]

%o (PARI) (3-exp(1))*(2-exp(1/2))^2 \\ _Charles R Greathouse IV_, Oct 31 2014

%Y Cf. A000670, A068996, A248788.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Oct 14 2014