A195388 Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(5),sqrt(7)).

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

Offset

1,2

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 7

Example

(C)=1.420620273394437946415144812116169231963535...

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(2)+sqrt(5)+sqrt(7)) \\ Charles R Greathouse IV, Apr 07 2026
(PARI) polrootsreal(x^7 - 7*x^6 - 31*x^5 + 129*x^4 - 32*x^3 - 24*x^2 - 160)[3] \\ Charles R Greathouse IV, Apr 07 2026

Crossrefs

Cf. A195284, A195386, A195387, A195389.

Sequence in context: A188595 A144102 A352750 * A255324 A328819 A330578

Adjacent sequences: A195385 A195386 A195387 * A195389 A195390 A195391

Keyword

nonn,cons

Author

Clark Kimberling, Sep 17 2011

Status

approved