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A195380 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(3),sqrt(1) right triangle ABC (angles 30, 60, 90). 3
5, 5, 7, 5, 7, 0, 1, 7, 6, 9, 1, 7, 0, 9, 3, 8, 0, 3, 7, 2, 1, 1, 2, 9, 1, 4, 6, 0, 4, 2, 9, 2, 3, 1, 8, 7, 2, 1, 1, 5, 2, 6, 1, 0, 0, 8, 9, 0, 3, 0, 5, 5, 9, 9, 2, 1, 6, 7, 9, 5, 5, 8, 9, 0, 9, 5, 8, 8, 2, 5, 6, 8, 1, 9, 4, 3, 6, 5, 6, 9, 3, 1, 0, 6, 8, 1, 8, 1, 7, 7, 7, 1, 2, 4, 7, 7, 1, 9, 3, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

Table of n, a(n) for n=0..99.

EXAMPLE

Philo(ABC,I)=0.55757017691709380372112914604292318...

MATHEMATICA

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

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) A195348 *)

N[x2, 100]

RealDigits[%] (* (B) A093821 *)

N[x3, 100]

RealDigits[%] (* (C) A120683 *)

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

RealDigits[%] (* A195380 *)

CROSSREFS

Cf. A195284.

Sequence in context: A122273 A052247 A088201 * A139261 A247649 A252655

Adjacent sequences:  A195377 A195378 A195379 * A195381 A195382 A195383

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified December 12 15:01 EST 2017. Contains 295939 sequences.