OFFSET
1,3
COMMENTS
See A195284 for definitions and a general discussion.
EXAMPLE
(C)=1.0803630269509058144061726281963757019894604...
MATHEMATICA
a = 1; b = 2; c = Sqrt[5]; 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) A195340 *)
N[x2, 100]
RealDigits[%] (* (B) A195341 *)
N[x3, 100]
RealDigits[%] (* (C) A195342 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195343 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 16 2011
STATUS
approved