login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195428 Decimal expansion of normalized Philo sum, Philo(ABC,G), where G=centroid of the 7,24,25 right triangle ABC. 5
5, 4, 7, 5, 5, 9, 7, 9, 0, 6, 2, 3, 7, 4, 8, 1, 9, 4, 9, 7, 8, 0, 9, 9, 1, 0, 4, 0, 6, 1, 8, 1, 2, 0, 6, 8, 9, 4, 1, 2, 4, 9, 9, 2, 3, 2, 7, 6, 0, 9, 9, 2, 1, 5, 8, 8, 6, 0, 5, 9, 9, 6, 3, 0, 0, 6, 9, 2, 9, 4, 7, 9, 9, 8, 3, 8, 6, 1, 5, 7, 2, 0, 0, 1, 0, 8, 4, 5, 1, 6, 4, 1, 2, 8, 5, 3, 7, 7, 6, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A195304 for definitions and a general discussion.

LINKS

Table of n, a(n) for n=0..99.

EXAMPLE

Philo(ABC,G)=0.5475597906237481949780991040618120...

MATHEMATICA

a = 7; b = 24; h = 2 a/3; k = b/3;

f[t_] := (t - a)^2 + ((t - a)^2) ((a*k - b*t)/(a*h - a*t))^2

s = NSolve[D[f[t], t] == 0, t, 150]

f1 = (f[t])^(1/2) /. Part[s, 4]

RealDigits[%, 10, 100] (* (A) A195425 *)

f[t_] := (t - a)^2 + ((t - a)^2) (k/(h - t))^2

s = NSolve[D[f[t], t] == 0, t, 150]

f2 = (f[t])^(1/2) /. Part[s, 4]

RealDigits[%, 10, 100] (* (B) A195426 *)

f[t_] := (b*t/a)^2 + ((b*t/a)^2) ((a*h - a*t)/(b*t - a*k))^2

s = NSolve[D[f[t], t] == 0, t, 150]

f3 = (f[t])^(1/2) /. Part[s, 1]

RealDigits[%, 10, 100] (* (C) A195427 *)

c = Sqrt[a^2 + b^2]; (f1 + f2 + f3)/(a + b + c)

RealDigits[%, 10, 100] (* Philo(ABC, G) A195428 *)

CROSSREFS

Cf. A195304.

Sequence in context: A177161 A154776 A188932 * A254373 A343564 A004446

Adjacent sequences:  A195425 A195426 A195427 * A195429 A195430 A195431

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 18 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)