A303985 Decimal expansion of 2*sin(45*Pi/128).

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

Offset

1,2

Comments

This is the value of R(45, x), with the monic Chebyshev polynomials of the first kind R (A127672) which has a solution (among the 45 real ones) x = 2*sin(Pi/128) = sqrt(2 - sqrt(2 + sqrt(2 + sqrt(2 + sqrt(2 + sqrt(2)))))) = A303984. See the comment in A303984 where this constant x appeared erroneously in a version of the exemplum secundum of Adrianus Romanus (Adriaan van Roomen). This appears in the first Romano link given below.

Links

Table of n, a(n) for n=1..105.

Adriano Romano Lovaniensi, Ideae Mathematicae, 1593.

Adriano Romano Lovaniensi, Ideae Mathematicae, 1593 [alternative link].

Index entries for sequences related to Chebyshev polynomials.

Formula

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

Equals 2 * Sum_{k >= 0} (-1)^k*(19*Pi/128)^(2*k)/(2*k)!. - Bruno Berselli, May 07 2018

Example

1.786448602391030640684832894986795956001251177997745579215866923036001176...

Mathematica

RealDigits[2*Sin[45*Pi/128], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)

Prog

(PARI) 2*sin(45*Pi/128) \\ Altug Alkan, May 06 2018

Crossrefs

Cf. A127672, A303984.

Sequence in context: A181624 A277683 A143300 * A242816 A333566 A093827

Adjacent sequences: A303982 A303983 A303984 * A303986 A303987 A303988

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, May 06 2018

Status

approved