OFFSET
0,1
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
Philo(ABC,I)=0.6011263969176532516541263787772610806686403999...
MATHEMATICA
a = Sqrt[3]; b = Sqrt[5]; c = Sqrt[8];
f = 2 a*b/(a + b + c);
x1 = Simplify[f*Sqrt[a^2 + (b + c)^2]/(b + c) ]
x2 = Simplify[f*Sqrt[b^2 + (c + a)^2]/(c + a) ]
x3 = f*Sqrt[2]
N[x1, 100]
RealDigits[%] (* (A) A195395 *)
N[x2, 100]
RealDigits[%] (* (B) A195396 *)
N[x3, 100]
RealDigits[%] (* (C) A195397 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195398 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
EXTENSIONS
a(99) corrected by Georg Fischer, Jul 18 2021
STATUS
approved