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A196772
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Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=sin(x-c), and 0 < x < 2*Pi; c = Pi - sqrt(r) - arccos(r-1), where r=(1+sqrt(5))/2 (the golden ratio).
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7
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9, 6, 5, 0, 1, 6, 1, 0, 9, 7, 7, 3, 3, 4, 2, 9, 1, 0, 0, 8, 2, 9, 0, 4, 1, 2, 5, 8, 8, 0, 0, 5, 2, 6, 7, 1, 0, 5, 0, 4, 6, 6, 7, 9, 6, 5, 7, 3, 4, 0, 4, 5, 0, 4, 7, 0, 2, 3, 0, 5, 7, 5, 6, 4, 1, 8, 5, 8, 9, 6, 1, 6, 9, 8, 6, 0, 9, 5, 7, 6, 9, 1, 9, 1, 5, 4, 0, 0, 2, 8, 8, 5, 2, 1, 7, 9, 4, 1, 0, 7
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..99.
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EXAMPLE
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c=0.965016109773342910082904125880052671050...
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MATHEMATICA
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Plot[{Sin[x + .97], 1/x}, {x, 0, Pi}]
r = GoldenRatio; x = Sqrt[r];
c = N[Pi - x - ArcCos[r - 1], 100]
RealDigits[c] (* A196772 *)
slope = N[-1/x^2, 100]
RealDigits[slope] (* 1-r *)
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CROSSREFS
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Cf. A195625, A196767.
Sequence in context: A021916 A154183 A200138 * A225406 A347330 A343947
Adjacent sequences: A196769 A196770 A196771 * A196773 A196774 A196775
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Oct 06 2011
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STATUS
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approved
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