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A318740
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Decimal expansion of (sqrt((5 - sqrt(5))/2) - (sqrt(5) - 1)/2) * exp(Pi/5).
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0
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1, 0, 4, 5, 0, 7, 7, 7, 1, 6, 1, 5, 8, 1, 3, 1, 5, 0, 8, 2, 4, 3, 0, 0, 4, 4, 2, 7, 8, 1, 6, 4, 0, 6, 6, 0, 5, 2, 3, 1, 2, 8, 9, 4, 6, 5, 6, 0, 8, 3, 7, 9, 9, 3, 1, 5, 1, 8, 0, 2, 9, 6, 1, 8, 0, 0, 6, 5, 2, 5, 2, 3, 7, 2, 2, 8, 3, 3, 8, 0, 4, 2, 3, 2, 1, 2, 2, 2, 3, 2
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OFFSET
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1,3
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COMMENTS
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The second part of Ramanujan's question 352 in the Journal of the Indian Mathematical Society (IV, 40) asked "Show that 1 / (1 - exp(-Pi) / (1 + exp(-2*Pi) / (1 - exp(-3*Pi) / (1 + ...)))) = (sqrt((5 - sqrt(5))/2) - (sqrt(5) - 1)/2) * exp(Pi/5)". Also stated in Ramanujan's first letter to G. H. Hardy in 1913. Corrected version from page 28 of Berndt, Choi and Kang, see links.
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LINKS
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EXAMPLE
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1.045077716158131508243004427816406605231289465608379931518029618...
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PROG
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(PARI) (sqrt((1/2)*(5-sqrt(5)))-(sqrt(5)-1)/2)*exp(Pi/5)
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CROSSREFS
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Cf. A091667 (part 1 of question 352).
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KEYWORD
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AUTHOR
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STATUS
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approved
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