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A247554 Decimal expansion of a(F_5), the maximum inradius of all triangles that lie in a regular pentagon of width 1. 0
2, 4, 4, 0, 1, 5, 5, 2, 8, 0, 9, 4, 1, 7, 1, 1, 1, 5, 3, 8, 1, 3, 7, 4, 4, 3, 3, 6, 8, 1, 2, 1, 6, 1, 2, 4, 2, 6, 4, 4, 3, 6, 9, 8, 8, 7, 0, 8, 1, 6, 5, 2, 8, 3, 2, 7, 4, 0, 2, 3, 2, 9, 6, 1, 1, 8, 8, 3, 5, 4, 8, 9, 2, 2, 1, 6, 3, 2, 5, 0, 7, 0, 8, 6, 6, 8, 4, 4, 8, 8, 4, 2, 6, 5, 4, 5, 8, 4, 7, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.19 Circumradius-Inradius Constants, p. 535.

LINKS

Table of n, a(n) for n=0..100.

FORMULA

Smallest positive root of the polynomial given in the Mathematica code.

EXAMPLE

0.2440155280941711153813744336812161242644369887...

MATHEMATICA

a[F5] = Root[5*x^8 - 175*x^7 + 611*x^6 - 816*x^5 + 720*x^4 - 280*x^3 + 160*x^2 - 96*x + 16, x, 1]; RealDigits[a[F5], 10, 101] // First

PROG

(PARI) solve(x=0, 1/4, 5*x^8 - 175*x^7 + 611*x^6 - 816*x^5 + 720*x^4 - 280*x^3 + 160*x^2 - 96*x + 16) \\ Michel Marcus, Sep 19 2014

CROSSREFS

Cf. A019827 (a(F_4)(unit square)).

Sequence in context: A258371 A111172 A173556 * A198786 A176531 A198362

Adjacent sequences:  A247551 A247552 A247553 * A247555 A247556 A247557

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Sep 19 2014

STATUS

approved

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Last modified June 18 03:46 EDT 2021. Contains 345098 sequences. (Running on oeis4.)