A195372 Decimal expansion of normalized Philo sum, Philo(ABC,I), where I=incenter of a 1,sqrt(2),sqrt(3) right triangle ABC.

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

Offset

0,1

Comments

See A195284 for definitions and a general discussion.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

Philo(ABC,I)=0.590568080015997134374704644164650566944103294...

Mathematica

a = 1; b = Sqrt[2]; c = Sqrt[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) A195369 *)
N[x2, 100]
RealDigits[%]    (* (B) A195370 *)
N[x3, 100]
RealDigits[%]    (* (C) A195371 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]    (* Philo(ABC, I) A195372 *)

Crossrefs

Cf. A195284, A195369, A195370, A195371.

Sequence in context: A269979 A102521 A198615 * A193017 A277651 A096789

Adjacent sequences: A195369 A195370 A195371 * A195373 A195374 A195375

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved