A195398 - OEIS

%I #7 Jul 18 2021 05:44:43

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

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

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

%N Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(3),sqrt(5),sqrt(8) right triangle ABC.

%C See A195284 for definitions and a general discussion.

%e Philo(ABC,I)=0.6011263969176532516541263787772610806686403999...

%t a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];

%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) A195395 *)

%t N[x2, 100]

%t RealDigits[%]    (* (B) A195396 *)

%t N[x3, 100]

%t RealDigits[%]    (* (C) A195397 *)

%t N[(x1 + x2 + x3)/(a + b + c), 100]

%t RealDigits[%]    (*  Philo(ABC,I) A195398 *)

%Y Cf. A195284.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 17 2011

%E a(99) corrected by _Georg Fischer_, Jul 18 2021