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A229923
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Decimal expansion of self-generating continued fraction with first term sqrt(2).
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1
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1, 9, 6, 7, 5, 5, 2, 4, 4, 5, 8, 7, 0, 3, 7, 4, 6, 2, 5, 9, 3, 9, 4, 8, 4, 9, 4, 4, 6, 0, 8, 0, 2, 5, 2, 2, 5, 0, 8, 4, 4, 1, 9, 7, 1, 4, 9, 1, 0, 8, 7, 8, 0, 6, 6, 8, 8, 6, 6, 7, 6, 7, 4, 1, 0, 9, 7, 7, 6, 9, 2, 3, 0, 9, 1, 9, 4, 6, 9, 4, 6, 2, 0, 2, 4, 1, 3, 4, 7, 7, 4, 1, 4, 5, 4, 8, 1, 9, 8, 2, 6, 7, 7, 7, 5
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OFFSET
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1,2
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COMMENTS
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For x > 0, define c(x,0) = x and c(x,n) = [c(x,0), ..., c(x,n-1)]. We call f(x) the self-generating continued fraction with first term x. See A229779.
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LINKS
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EXAMPLE
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f(sqrt(2)) = 1.967552445870374625939484944608025225084419714910878...
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MATHEMATICA
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$MaxExtraPrecision = Infinity; z = 300; c[x_, 0] := x; c[x_, n_] :=
c[x, n] = FromContinuedFraction[Table[c[x, k], {k, 0, n - 1}]]; x = N[Sqrt[2], 300]; t1 = Table[c[x, k], {k, 0, z}]; u = N[c[x, z], 120] (* A229923 *)
RealDigits[u]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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