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A195372 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(2),sqrt(3) right triangle ABC. 5
5, 9, 0, 5, 6, 8, 0, 8, 0, 0, 1, 5, 9, 9, 7, 1, 3, 4, 3, 7, 4, 7, 0, 4, 6, 4, 4, 1, 6, 4, 6, 5, 0, 5, 6, 6, 9, 4, 4, 1, 0, 3, 2, 9, 4, 1, 9, 3, 4, 2, 2, 8, 8, 8, 7, 8, 2, 6, 1, 4, 8, 0, 1, 3, 7, 9, 5, 6, 6, 0, 0, 7, 2, 4, 2, 4, 6, 8, 5, 7, 1, 9, 9, 1, 0, 8, 4, 5, 3, 9, 5, 3, 6, 8, 5, 5, 6, 5, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

EXAMPLE

Philo(ABC,I)=0.590568080015997134374704644164650566944103294...

MATHEMATICA

a = 1; b = Sqrt[2]; c = Sqrt[3];

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) A195369 *)

N[x2, 100]

RealDigits[%]    (* (B) A195370 *)

N[x3, 100]

RealDigits[%]    (* (C) A195371 *)

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

RealDigits[%]    (* Philo(ABC, I) A195372 *)

CROSSREFS

Cf. A195284, A195369, A195370, A195371.

Sequence in context: A269979 A102521 A198615 * A193017 A277651 A096789

Adjacent sequences:  A195369 A195370 A195371 * A195373 A195374 A195375

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified August 26 01:34 EDT 2019. Contains 326324 sequences. (Running on oeis4.)