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A231097
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Decimal expansion of the power tower of the ratio e/Pi.
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2
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8, 8, 0, 3, 6, 7, 7, 7, 8, 9, 8, 1, 7, 3, 4, 6, 2, 1, 8, 2, 6, 7, 4, 9, 8, 5, 2, 8, 5, 4, 4, 2, 0, 7, 1, 1, 4, 5, 9, 5, 7, 9, 9, 6, 3, 4, 7, 6, 6, 3, 4, 9, 2, 9, 1, 6, 4, 8, 1, 9, 6, 3, 6, 2, 0, 5, 7, 2, 4, 7, 6, 6, 4, 9, 9, 9, 0, 3, 9, 9, 4, 2, 0, 4, 2, 8, 3, 9, 1, 9, 8, 4, 2, 2, 0, 8, 1, 8, 7, 4, 6, 6, 1, 5, 9
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OFFSET
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0,1
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COMMENTS
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This infinite tetration limit of (e/Pi)^^n is also the only solution of x*(Pi/e)^x = 1.
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LINKS
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FORMULA
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When 1/e^e <= c < 1, then c^c^c^... = LambertW(log(1/c))/log(1/c).
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EXAMPLE
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0.88036777898173462182674985...
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MATHEMATICA
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RealDigits[ProductLog[Log[Pi] - 1]/(Log[Pi] - 1), 10, 120][[1]] (* Amiram Eldar, May 17 2023 *)
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PROG
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(PARI) lambertw(log(Pi)-1)/(log(Pi)-1)
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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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