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%I #8 Dec 24 2017 09:27:25
%S 1,0,4,5,8,3,1,3,7,9,9,7,9,9,5,5,8,7,4,9,4,8,7,2,0,5,7,5,7,0,3,4,1,1,
%T 6,8,1,4,2,4,8,5,2,0,4,7,4,4,8,0,2,4,4,0,9,4,4,5,3,8,9,4,5,8,9,0,4,0,
%U 7,2,1,2,7,2,0,5,8,6,7,2,9,0,3,5,6,3,1,8,0,3,1,7,9,4,4,5,7,4,1,1
%N Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)).
%C See A195284 for definitions and a general discussion.
%H G. C. Greubel, <a href="/A195386/b195386.txt">Table of n, a(n) for n = 1..10000</a>
%e (A)=1.0458313799799558749487205757034116814248520474480...
%t a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];
%t f = 2 a*b/(a + b + c);
%t x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
%t x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
%t x3 = f*Sqrt[2]
%t N[x1, 100]
%t RealDigits[%] (* (A) A195386 *)
%t N[x2, 100]
%t RealDigits[%] (* (A) A195387 *)
%t N[x3, 100]
%t RealDigits[%] (* (A) A195388 *)
%t N[(x1 + x2 + x3)/(a + b + c), 100]
%t RealDigits[%] (* Philo(ABC,I) A195389 *)
%Y Cf. A195284, A195887, A195888, A195389.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Sep 17 2011
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