

A228787


Decimal expansion of 2*sin(Pi/17), the ratio side/R in the regular 17gon inscribed in a circle of radius R.


7



3, 6, 7, 4, 9, 9, 0, 3, 5, 6, 3, 3, 1, 4, 0, 6, 6, 3, 1, 4, 8, 8, 1, 7, 6, 7, 9, 2, 4, 1, 4, 5, 5, 1, 6, 4, 9, 7, 8, 2, 7, 7, 0, 4, 7, 6, 8, 8, 9, 9, 8, 8, 1, 1, 7, 0, 1, 3, 0, 1, 7, 1, 5, 4, 9, 7, 8, 2, 9, 8, 5, 6, 5, 0, 6, 1, 0, 0, 3, 4, 6, 0, 6, 1, 2, 0, 2, 3, 9, 0, 2, 4, 2, 1, 4, 6, 0, 9, 7, 1, 8, 5, 9, 3, 5, 9, 5
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OFFSET

0,1


COMMENTS

s(17) := 2*sin(Pi/17) is an algebraic integer of degree 16 (over the rationals). Its minimal polynomial is 17  204*x^2 + 714*x^4  1122*x^6 + 935*x^8  442*x^10 + 119*x^12  17*x^14 + x^16. Its coefficients in the power basis of the algebraic number field Q(2*cos(Pi/34)) are [0, 15, 0, 140, 0, 378, 0, 450, 0, 275, 0, 90, 0, 15, 0, 1] (see row l = 8 of A228785). The decimal expansion of 2*cos(Pi/34) is given in A228788.
The continued fraction expansion starts with 0; 2, 1, 2, 1, 1, 2, 2, 2, 1, 5, 1, 3, 2, 2, 2, 1, 1, 43, 3, 1, 5, 2, 17, 2, ...
Gauss' formula for cos(2*Pi/17), given in A210644, can be inserted into s(17) = sqrt(2*(1  cos(2*Pi/17))).
Since 17 is a Fermat prime, this number is constructible and can be written as an expression containing just integers, the basic four arithmetic operations, and square roots. See A003401 for more details.  Stanislav Sykora, May 02 2016


LINKS

Table of n, a(n) for n=0..106.
Kival Ngaokrajang, Illustration of the ratio side/R in the regular 17gon inscribed in a circle of radius R


FORMULA

s(17) = 2*sin(Pi/17) = 0.367499035633140663148817679...
Equals sqrt(342*sqrt(17)2*sqrt(342*sqrt(17))4*sqrt(17+3*sqrt(17)sqrt(342*sqrt(17))2*sqrt(34+2*sqrt(17))))/4.  Stanislav Sykora, May 02 2016


MATHEMATICA

RealDigits[2Sin[Pi/17], 10, 100][[1]] (* Alonso del Arte, Jan 01 2014 *)


PROG

(PARI) 2*sin(Pi/17) \\ Charles R Greathouse IV, Nov 12 2014


CROSSREFS

Cf. A003401, A019434, A210644, A228785, A228788.
Sequence in context: A098990 A162195 A117361 * A245220 A165952 A156648
Adjacent sequences: A228784 A228785 A228786 * A228788 A228789 A228790


KEYWORD

nonn,cons


AUTHOR

Wolfdieter Lang, Oct 07 2013


EXTENSIONS

Offset corrected by Rick L. Shepherd, Jan 01 2014


STATUS

approved



