A195343 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,2,sqrt(5) right triangle ABC.

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

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)=0.5277526336077103561182142902939495223804021352...

Mathematica

a = 1; b = 2; c = Sqrt[5]; 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) A195340 *)
N[x2, 100]
RealDigits[%] (* (B) A195341 *)
N[x3, 100]
RealDigits[%] (* (C) A195342 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%] (* Philo(ABC, I) A195343 *)

Crossrefs

Cf. A195284.

Sequence in context: A354827 A364521 A253545 * A074454 A256110 A267211

Adjacent sequences: A195340 A195341 A195342 * A195344 A195345 A195346

Keyword

nonn,cons

Author

Clark Kimberling, Sep 16 2011

Extensions

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

Status

approved