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A058281
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Continued fraction for square root of e.
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10
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1, 1, 1, 1, 5, 1, 1, 9, 1, 1, 13, 1, 1, 17, 1, 1, 21, 1, 1, 25, 1, 1, 29, 1, 1, 33, 1, 1, 37, 1, 1, 41, 1, 1, 45, 1, 1, 49, 1, 1, 53, 1, 1, 57, 1, 1, 61, 1, 1, 65, 1, 1, 69, 1, 1, 73, 1, 1, 77, 1, 1, 81, 1, 1, 85, 1, 1, 89, 1, 1, 93, 1, 1, 97, 1, 1, 101, 1, 1, 105, 1, 1, 109, 1, 1, 113, 1, 1
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OFFSET
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0,5
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COMMENTS
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sqrt(e) = 1.64872127070012814684865078781416357165377610071014801157507... - Harry J. Smith, May 01 2009
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LINKS
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FORMULA
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a(3k+1) = 4k+1, a(i) = 1 otherwise.
G.f.: -(x^2-x+1)*(x^3-2*x^2-2*x-1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, Jun 24 2013
E.g.f.: exp(-x/2)*(exp(3*x/2)*(5 + 4*x) + (4 + 8*x)*cos(sqrt(3)*x/2) - 4*sqrt(3)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, May 05 2022
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EXAMPLE
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sqrt(e) = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(5 + ...)))). - Harry J. Smith, May 01 2009
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MATHEMATICA
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ContinuedFraction[ Sqrt[E], 100]
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PROG
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(PARI) contfrac(sqrt(exp(1)))
(PARI) { allocatemem(932245000); default(realprecision, 60000); x=contfrac(sqrt(exp(1))); for (n=1, 20001, write("b058281.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 01 2009
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CROSSREFS
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Cf. A019774 for decimal expansion of sqrt(e).
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KEYWORD
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cofr,nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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