A195385 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 2,sqrt(5),3 right triangle ABC.

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

Table of n, a(n) for n=0..104.

Example

Philo(ABC,I)=0.6115583512796641306567793224288443270777...

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 *)

Crossrefs

Cf. A195284.

Sequence in context: A335505 A182429 A325385 * A319990 A138073 A131778

Adjacent sequences: A195382 A195383 A195384 * A195386 A195387 A195388

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Extensions

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

Status

approved