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A245279 Decimal expansion of a1, the first of two constants associated with Djokovic's conjecture on an integral inequality. 1

%I

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

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

%U 8,8,3,9,7,7,1,6,0,0,9,2,1,1,7,8,4,8,9,9,7,8,0,4,3,7,2,6,0,9,6,9,7,4,0

%N Decimal expansion of a1, the first of two constants associated with Djokovic's conjecture on an integral inequality.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.1.1 Djokovic's Conjecture, p. 210.

%F Positive root of 12*x^3 - 16*x^2 + 8*x - 1.

%F Equals (r - 8/r + 8)/18, where r = (27*sqrt(17)-109)^(1/3).

%e 0.1824878875219793398416793914878206648753039383250540321198664994565...

%t a1 = Root[12*x^3 - 16*x^2 + 8*x - 1, x, 1]; RealDigits[a1, 10, 103] // First

%Y Cf. A245280.

%K nonn,cons,easy

%O 0,2

%A _Jean-Fran├žois Alcover_, Jul 16 2014

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