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A194807
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Decimal expansion of 1/(e-2).
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9
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1, 3, 9, 2, 2, 1, 1, 1, 9, 1, 1, 7, 7, 3, 3, 2, 8, 1, 4, 3, 7, 6, 5, 5, 2, 8, 7, 8, 4, 7, 9, 8, 1, 6, 5, 2, 8, 3, 7, 3, 9, 7, 8, 3, 8, 5, 3, 1, 5, 2, 8, 7, 1, 2, 3, 5, 9, 1, 3, 2, 4, 5, 6, 7, 0, 8, 3, 2, 7, 9, 5, 7, 0, 4, 6, 1, 6, 1, 0, 9, 2, 6, 6, 9, 1, 7, 1, 0, 5, 8, 7, 2, 6, 7, 6, 1, 2, 9, 9, 8, 8, 8, 8, 5, 6
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OFFSET
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1,2
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COMMENTS
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The value of the continued fraction 1+1/(2+2/(3+3/(4+4/(5+5/(6+6/(...)))))).
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LINKS
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FORMULA
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Define s(n) = Sum_{k = 2..n} 1/k! for n >= 2. Then 1/(e - 2) = 2! - Sum_ {n >= 2} 1/( (n+1)!*s(n)*s(n+1) ) is a rapidly converging series of rationals. Cf.A073333.Equivalently, 1/(e - 2) = 2! - 2!/(1*4) - 3!/(4*17) - 4!/(17*86) -..., where [1, 4, 17, 86,... ] isA056542.Cf.A002627andA185108.-Peter Bala,Oct 09 2013
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EXAMPLE
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1.392211191177332814376552878479816528373978385315...
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MATHEMATICA
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RealDigits[1/(E - 2), 10, 105][[1]] (*T. D. Noe,May 07 2012 *)
Fold[Function[#2 + #2/#1], 1, Reverse[Range[100]]] // N[#, 105]& // RealDigits // First (*Jean-François Alcover,Sep 19 2014 *)
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PROG
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(PARI)
default(realprecision, 110);
1/(exp(1)-2)
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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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