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A303985
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Decimal expansion of 2*sin(45*Pi/128).
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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
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EXAMPLE
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1.786448602391030640684832894986795956001251177997745579215866923036001176...
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MATHEMATICA
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RealDigits[2*Sin[45*Pi/128], 10, 120][[1]] (* Amiram Eldar, Jun 26 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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