

A303983


Decimal expansion of 2*sin((37/384)*Pi).


1



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

0,1


COMMENTS

This constant is a solution x of R(45, x) = sqrt(2 + sqrt(2  sqrt(2  sqrt(2  sqrt(2  sqrt(2)))))) = A303982, with the monic Chebyshev polynomial of the first kind, called R, with coefficients given in A127672. This polynomial with the given value appears in the historic problem (exemplum secundum) posed by Adriaan van Roomen (Adrianus Romanus) in his Ideae mathematicae from 1593. However, the two solutions given there (in two different printings) are incorrect. See A303982 for comments and the Vieta link.


LINKS

Table of n, a(n) for n=0..105.
Adriano Romano Lovaniensi, Ideae Mathematicae, 1593.
Adriano Romano Lovaniensi, Ideae Mathematicae, 1593 [alternative link with other exemplum 2].
Index entries for sequences related to Chebyshev polynomials.


FORMULA

2*sin((37/384)*Pi) = sqrt(2  sqrt(2 + sqrt(2  sqrt(2 + sqrt(2  sqrt(2 + sqrt(3))))))).


EXAMPLE

0.59620765008547968506921945135201382172676759902006770333178792164608434044...


MAPLE

a:=evalf(2*sin((37/384)*Pi), 160): b:=[]: for n from 1 to 106 do
b:=[op(b), trunc(10*a)]: a:=evalf(frac(10*a), 109): od: print(op(b));
# Paolo P. Lava, May 07 2018


PROG

(PARI) 2*sin(37*Pi/384) \\ Altug Alkan, May 06 2018


CROSSREFS

Cf. A127672, A303982.
Sequence in context: A134879 A051158 A117605 * A073003 A087498 A274633
Adjacent sequences: A303980 A303981 A303982 * A303984 A303985 A303986


KEYWORD

nonn,cons,easy


AUTHOR

Wolfdieter Lang, May 04 2018


STATUS

approved



