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A254604
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The decimal expansion of the half of a single half-wave constant x.
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0
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3, 6, 8, 3, 0, 5, 3, 9, 0, 5, 9, 6, 6, 6, 1, 3, 9, 9, 9, 4, 6, 9, 9, 1, 6, 8, 9, 9, 3, 2, 3, 3, 6, 3, 3, 8, 0, 8, 0, 7, 6, 0, 1, 5, 8, 2, 0, 9, 7, 9, 2, 7, 2, 7, 2, 7, 6, 8, 9, 9, 4, 9, 6, 5, 5, 3, 4, 6, 4, 2, 3, 5, 5, 5, 5, 2, 8, 6, 9, 4, 5, 0, 1, 8, 1, 8, 2, 5, 4, 5, 7, 0, 4, 7, 9, 1, 1, 5, 8, 4, 3, 1, 8, 1, 2, 6, 7, 6, 7, 3, 9, 6, 5, 9, 1, 5, 0, 4, 9, 4, 7
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OFFSET
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0,1
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COMMENTS
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By the definition this constant takes the values 0 < x < Pi such that the horizontal line y = sin x divides the region bounded by the sine curve and the interval [0,Pi] on the x-axis into two figures of equal areas.
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LINKS
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Table of n, a(n) for n=0..120.
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FORMULA
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2*cos(x) - (Pi - 2*x)*sin(x) = 1, 0 < x < Pi.
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EXAMPLE
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x = 0.368305390596661399946991689932336338080760158209792727276899496553...
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MATHEMATICA
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FindRoot[2 Cos[x] - (Pi - 2 x) Sin[x] - 1 == 0, {x, 0, Pi}, WorkingPrecision -> 150] (* Bruno Berselli, Feb 03 2015 *)
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PROG
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(PARI) solve(x=0, Pi, 2*cos(x) - (Pi - 2*x)*sin(x) - 1) \\ Michel Marcus, Feb 03 2015
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CROSSREFS
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Sequence in context: A181917 A157032 A295655 * A278498 A011334 A200340
Adjacent sequences: A254601 A254602 A254603 * A254605 A254606 A254607
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KEYWORD
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nonn,cons
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AUTHOR
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Roman Witula, Feb 02 2015
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STATUS
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approved
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