A195386 Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)).

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

Offset

1,3

Comments

See A195284 for definitions and a general discussion.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 8

Example

(A)=1.0458313799799558749487205757034116814248520474480...

Mathematica

a = Sqrt[2]; b = Sqrt[5]; c = Sqrt[7];
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) A195386 *)
N[x2, 100]
RealDigits[%]   (* (A) A195387 *)
N[x3, 100]
RealDigits[%]   (* (A) A195388 *)
N[(x1 + x2 + x3)/(a + b + c), 100]
RealDigits[%]   (* Philo(ABC, I) A195389 *)

Prog

(PARI) 4*sqrt(5*sqrt(35) + 35)/(sqrt(10) + sqrt(14) + 2*sqrt(35) + 12) \\ Charles R Greathouse IV, Apr 05 2026
(PARI) polrootsreal(x^8 - 672*x^6 + 82656*x^4 - 376320*x^2 + 313600)[5] \\ Charles R Greathouse IV, Apr 05 2026

Crossrefs

Cf. A195284, A195387, A195388, A195389.

Sequence in context: A180307 A263208 A010477 * A384461 A259468 A394004

Adjacent sequences: A195383 A195384 A195385 * A195387 A195388 A195389

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved