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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299695 Decimal expansion of smallest disk radius for which six equal disks can cover the unit disk. 0
5, 5, 5, 9, 0, 5, 2, 1, 1, 4, 1, 6, 5, 8, 8, 7, 0, 4, 8, 2, 6, 2, 9, 5, 5, 5, 0, 6, 9, 6, 5, 9, 3, 0, 2, 2, 9, 6, 1, 3, 8, 6, 1, 1, 8, 1, 9, 7, 4, 7, 4, 4, 6, 6, 3, 4, 1, 2, 6, 9, 4, 6, 1, 6, 7, 4, 5, 3, 0, 8, 4, 4, 4, 3, 9, 2, 8, 6, 7, 8, 2, 2, 2, 8, 5, 2, 5, 9, 4, 2, 4, 9, 4, 8, 5, 4, 8, 4, 7, 4, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The largest disk that can be covered by six unit disks has radius 1/r = 1.79886782...

Piezas (see Mathematics Stack Exchange link) notes that the minimal polynomials for both this constant and A133077 have unsolvable Galois groups.

LINKS

Table of n, a(n) for n=0..101.

Erich Friedman, Circles Covering Circles

Jeremy Tan, What is the exact value of the radius in the Six Disks Problem?, Mathematics Stack Exchange, Feb 15 2018

Jeremy Tan, Python and Singular programs

Eric Weisstein's World of Mathematics, Disk Covering Problem

FORMULA

r is the smallest positive root of 7841367r^18 - 33449976r^16 + 62607492r^14 - 63156942r^12 + 41451480r^10 - 19376280r^8 + 5156603r^6 - 746832r^4 + 54016r^2 + 3072.

EXAMPLE

0.55590521141658870482629555069659...

MATHEMATICA

First@ RealDigits@ N[Root[7841367x^18 -33449976x^16 +62607492x^14 -63156942x^12 +41451480x^10 -19376280x^8 +5156603x^6 -746832x^4 +54016x^2 +3072, x, 3], 102]

PROG

(PARI) polrootsreal(7841367*x^18 -33449976*x^16 +62607492*x^14 -63156942*x^12 +41451480*x^10 -19376280*x^8 +5156603*x^6 -746832*x^4 +54016*x^2 +3072)[3]

CROSSREFS

Cf. A133077 (five disks).

Sequence in context: A204911 A087516 A194428 * A135089 A127310 A214925

Adjacent sequences:  A299692 A299693 A299694 * A299696 A299697 A299698

KEYWORD

nonn,cons

AUTHOR

Jeremy Tan, Feb 16 2018

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 September 25 12:23 EDT 2020. Contains 337343 sequences. (Running on oeis4.)