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A195381 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(2,sqrt(5),3). 5
1, 3, 2, 3, 1, 6, 9, 0, 7, 6, 4, 9, 9, 2, 1, 4, 9, 9, 5, 4, 0, 3, 0, 7, 3, 6, 2, 4, 7, 3, 5, 2, 1, 7, 4, 8, 9, 9, 9, 5, 4, 9, 4, 0, 5, 6, 1, 3, 9, 5, 5, 1, 0, 5, 7, 5, 7, 9, 8, 4, 7, 1, 7, 2, 2, 4, 2, 3, 1, 5, 9, 5, 8, 7, 8, 9, 4, 2, 1, 0, 7, 7, 7, 2, 4, 1, 5, 1, 1, 8, 3, 4, 1, 3, 0, 7, 2, 2, 0, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A195284 for definitions and a general discussion.

LINKS

Table of n, a(n) for n=1..100.

FORMULA

Equals sqrt(12)/phi^2, where phi = A001622. - Jon Maiga, Nov 14 2018

EXAMPLE

(A)=1.32316907649921499540307362473521748999...

MATHEMATICA

a = 2; b = Sqrt[5]; c = 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) A195381 *)

N[x2, 100]

RealDigits[%]   (* (B) A195383 *)

N[x3, 100]

RealDigits[%]   (* (C) A195384 *)

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

RealDigits[%]   (* Philo(ABC, I) A195385 *)

RealDigits[Sqrt[12] / ((1 + Sqrt[5]) / 2)^2, 10, 100] (* Vincenzo Librandi, Nov 15 2018 *)

PROG

(MAGMA) Sqrt(12) / ((1 + Sqrt(5)) / 2)^2; // Vincenzo Librandi, Nov 15 2018

CROSSREFS

Cf. A195284, A195383, A195384, A195385.

Sequence in context: A165026 A289773 A197475 * A144558 A307551 A220344

Adjacent sequences:  A195378 A195379 A195380 * A195382 A195383 A195384

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 17 2011

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)