A195406 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of the right triangle ABC having sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).

6, 0, 2, 5, 6, 1, 3, 9, 1, 2, 8, 6, 1, 1, 4, 8, 6, 1, 7, 9, 4, 1, 5, 7, 2, 2, 9, 1, 1, 6, 8, 4, 7, 1, 7, 8, 6, 3, 8, 5, 7, 4, 5, 3, 6, 2, 9, 6, 6, 4, 0, 6, 1, 3, 7, 0, 4, 5, 5, 2, 3, 8, 4, 6, 2, 3, 4, 6, 6, 8, 3, 6, 1, 2, 1, 4, 7, 7, 2, 7, 4, 9, 7, 8, 2, 7, 2, 9, 9, 9, 0, 1, 8, 7, 3, 1, 3, 3, 7, 5, 6

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=0..100.

Example

Philo(ABC,I)=0.6025613912861148617941572291168471786...

Mathematica

a = 1; b = Sqrt[c]; c = (1 + Sqrt[5])/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) A195403 *)
N[x2, 100]
RealDigits[%]    (* (B) A195404 *)
N[x3, 100]
RealDigits[%]    (* (C) A195405 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC, I) A195406 *)

Crossrefs

Cf. A195284.

Sequence in context: A261166 A021170 A329093 * A021628 A371923 A201331

Adjacent sequences: A195403 A195404 A195405 * A195407 A195408 A195409

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Extensions

a(99) corrected by Georg Fischer, Jul 18 2021

Status

approved