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A299695
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Decimal expansion of smallest disk radius for which six equal disks can cover the unit disk.
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0
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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
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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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/Singular program
Eric Weisstein's World of Mathematics, Disk Covering Problem
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FORMULA
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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.
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EXAMPLE
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0.55590521141658870482629555069659...
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MATHEMATICA
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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]
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PROG
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(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]
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CROSSREFS
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Cf. A133077 (five disks).
Sequence in context: A204911 A087516 A194428 * A135089 A127310 A214925
Adjacent sequences: A299692 A299693 A299694 * A299696 A299697 A299698
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KEYWORD
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nonn,cons
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AUTHOR
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Jeremy Tan, Feb 16 2018
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STATUS
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approved
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