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A137218
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Decimal expansion of the argument of -1+i2.
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1
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2, 0, 3, 4, 4, 4, 3, 9, 3, 5, 7, 9, 5, 7, 0, 2, 7, 3, 5, 4, 4, 5, 5, 7, 7, 9, 2, 3, 1, 0, 0, 9, 6, 5, 8, 4, 4, 1, 2, 7, 1, 2, 1, 7, 5, 3, 9, 7, 3, 6, 7, 3
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OFFSET
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1,1
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COMMENTS
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Gives closed forms for many arctangent values.
ArcTan[2]=Pi-a ArcTan[1/2]=a-Pi/2
ArcTan[3]=a-Pi/4 ArcTan[1/3]=3Pi/4-a
ArcTan[7]=7Pi/4-2a ArcTan[1/7]=2a-5Pi/4
ArcTan[4/3]=2a-Pi ArcTan[3/4]=3Pi/2-2a
There is the sum
a=Sum[((2+8r)/(8n+1)+(1-8r)/(8n+2)-4r/(8n+3)-(1+8r)/(8n+4)-(1/2+2r)/(8n+5)-(3/4+2r)/(8n+6)+r/(8n+7))/16^n,n,1,Infinity]
Dihedral angle in the dodecahedron (radians). - R. J. Mathar, Mar 24 2012
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LINKS
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Table of n, a(n) for n=1..52.
Wikipedia, Dodecahedron
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FORMULA
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Equals Pi-arctan(2)= A000796 - A105199 = 2*A195723.
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EXAMPLE
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2.0344439357957027354455779231...
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CROSSREFS
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Sequence in context: A066439 A213859 A101336 * A087819 A066246 A198370
Adjacent sequences: A137215 A137216 A137217 * A137219 A137220 A137221
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KEYWORD
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cons,nonn
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AUTHOR
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Matt Rieckman (mjr162006(AT)yahoo.com), Mar 06 2008
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EXTENSIONS
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Corrected a typo in the sequence Matt Rieckman (mjr162006(AT)yahoo.com), Feb 05 2010
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STATUS
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approved
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