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A195398
Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(3),sqrt(5),sqrt(8) right triangle ABC.
5
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, 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, 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
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
Cf. A195284.
Sequence in context: A158781 A293299 A293486 * A063085 A020796 A011253
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Sep 17 2011
EXTENSIONS
a(99) corrected by Georg Fischer, Jul 18 2021
STATUS
approved