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A053978
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Continued fraction expansion of limit_{m->infinity} [r_m], where r_1=1, r_{m+1}= r_1 + 1/(r_2 + 1/(r_3 +...1/(r_{m-1} + 1/r_m)...)).
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4
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1, 1, 2, 2, 8, 59, 1, 46, 1, 2, 3, 22, 1, 60, 1, 1, 1, 4, 1, 6, 2, 1, 1, 3, 4, 1, 2, 6, 1, 25, 2, 1, 2, 7, 3, 11, 1, 1, 20, 1, 3, 1, 1, 3, 1, 11, 1, 2, 31, 3, 2, 2, 5, 1, 1, 3, 3, 11, 1, 2, 4, 2, 1, 1, 1, 6, 3, 3, 3, 15, 2, 1, 5, 2, 2, 3, 2, 1, 1, 3, 2, 2, 8, 1, 7, 1, 4, 1, 4, 2, 2, 5, 2, 1, 4, 1, 19, 1
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OFFSET
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0,3
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COMMENTS
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limit_{m -> infinity} [r_m] =1.7118691868...
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LINKS
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MATHEMATICA
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digits = 100; Clear[r]; r[1]=1; r[m_] := r[m] = FromContinuedFraction[Array[r, m-1]] // N[#, 2*digits]&; k=20; While[ContinuedFraction[r[k], digits] != ContinuedFraction[r[k-1], digits], k++; Print["k = ", k]]; ContinuedFraction[r[k], digits] (* Jean-François Alcover, Dec 11 2014 *)
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CROSSREFS
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KEYWORD
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cofr,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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