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A369499
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Decimal expansion of exp(sqrt(3)*Pi/18)/3^(1/4).
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0
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1, 0, 2, 8, 0, 3, 2, 5, 4, 1, 6, 8, 9, 5, 7, 6, 7, 7, 0, 4, 6, 2, 8, 8, 4, 3, 5, 7, 8, 5, 7, 7, 2, 1, 6, 7, 7, 8, 9, 2, 4, 1, 8, 6, 2, 6, 5, 4, 0, 0, 2, 2, 3, 9, 5, 4, 0, 6, 8, 8, 1, 6, 2, 8, 0, 3, 8, 0, 5, 3, 4, 7, 2, 2, 7, 0, 9, 7, 9, 0, 1, 0, 6, 6, 7, 1, 0, 7, 6, 7, 2, 0, 0, 9, 7, 0, 6, 9, 1, 7, 1, 3, 0, 5, 0, 3, 3, 4, 0, 3, 4, 5, 6, 1, 5, 0, 6, 7, 0, 8
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OFFSET
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1,3
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LINKS
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Albert Stadler, Problem 11677, Problems and Solutions, The American Mathematical Monthly, Vol. 119, No. 10 (2012), p. 880; Dedekind eta Function Disguised, Solution to Problem 11677 by Radouan Boukharfane, ibid., Vol. 121, No. 10 (December 2014), pp. 951-952. Note that the problem appeared with typos.
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FORMULA
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Equals Product_{k>=1} (1 + 2*exp(-k*Pi*sqrt(3)) * cosh(k*Pi/sqrt(3))) (Stadler, 2012).
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EXAMPLE
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1.02803254168957677046288435785772167789241862654002...
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MATHEMATICA
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RealDigits[Exp[Sqrt[3]*Pi/18]/3^(1/4), 10, 120][[1]]
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PROG
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(PARI) exp(sqrt(3)*Pi/18)/sqrtn(3, 4)
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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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