A303983 Decimal expansion of 2*sin((37/384)*Pi).

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

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

Equals sqrt(2 - sqrt(2 + sqrt(2 - sqrt(2 + sqrt(2 - sqrt(2 + sqrt(3))))))).

Example

0.59620765008547968506921945135201382172676759902006770333178792164608434044...

Mathematica

RealDigits[2*Sin[37*Pi/384], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)

Prog

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

Crossrefs

Cf. A127672, A303982.

Sequence in context: A134879 A051158 A117605 * A073003 A344093 A087498

Adjacent sequences: A303980 A303981 A303982 * A303984 A303985 A303986

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, May 04 2018

Status

approved