A195402 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a sqrt(7),3,4 right triangle ABC.

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

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)=0.6108897803863800074424128886740422330...

Mathematica

a = Sqrt[7]; b = 3; c = 4;
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) A195399 *)
N[x2, 100]
RealDigits[%]    (* (B) A195400 *)
N[x3, 100]
RealDigits[%]    (* (C) A195401 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (*  Philo(ABC, I) A195402 *)

Crossrefs

Cf. A195284.

Sequence in context: A355415 A262704 A335245 * A176402 A204013 A127573

Adjacent sequences: A195399 A195400 A195401 * A195403 A195404 A195405

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved