login
A303985
Decimal expansion of 2*sin(45*Pi/128).
1
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
Adriano Romano Lovaniensi, Ideae Mathematicae, 1593.
Adriano Romano Lovaniensi, Ideae Mathematicae, 1593 [alternative link].
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
Sequence in context: A181624 A277683 A143300 * A242816 A333566 A093827
KEYWORD
nonn,cons,easy
AUTHOR
Wolfdieter Lang, May 06 2018
STATUS
approved