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 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 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

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