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A255240 Decimal expansion of 1/(2 cos(2 Pi/7)). 1
5, 5, 4, 9, 5, 8, 1, 3, 2, 0, 8, 7, 3, 7, 1, 1, 9, 1, 4, 2, 2, 1, 9, 4, 8, 7, 1, 0, 0, 6, 4, 1, 0, 4, 8, 1, 0, 6, 7, 2, 8, 8, 8, 6, 2, 4, 7, 0, 9, 1, 0, 0, 8, 9, 3, 7, 6, 0, 2, 5, 9, 6, 8, 2, 0, 5, 1, 5, 7, 5, 3, 5, 9, 4, 2, 9, 0, 5, 3, 6, 1, 8, 5, 0, 8, 3, 7, 8, 9, 4, 7, 8, 3, 8, 5, 4, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the decimal expansion of t = 1/rho(7) = 2 + rho(7) - rho(7)^2 with rho(7) = 2*cos(2*Pi/7) the length ratio of the smaller diagonal and the side of a regular heptagon. See A160389 for the decimal expansion of rho(7).

t satisfies the cubic equation t^3 - 2*t^2 - t + 1 = 0.

t = 1/rho(7) is the slope tan(alpha) appearing in Archimedes's neusis construction of the regular heptagon. The corresponding angle alpha is approximately 29,028 degrees. See the link, Figure 1, also for references.

LINKS

Table of n, a(n) for n=1..97.

Wolfdieter Lang, Archimedes's Construction of the Regular Heptagon.

FORMULA

1/rho(7) = 1/(2*cos(2*Pi/7)) = 0.55495813208...

CROSSREFS

Cf. A160389, A231187.

Sequence in context: A011189 A261346 A011409 * A168578 A019253 A019173

Adjacent sequences:  A255237 A255238 A255239 * A255241 A255242 A255243

KEYWORD

nonn,cons

AUTHOR

Wolfdieter Lang, Mar 12 2015

STATUS

approved

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Last modified January 24 16:34 EST 2020. Contains 331207 sequences. (Running on oeis4.)