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A053978 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)...)). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

limit_{m -> infinity} [r_m] =1.7118691868...

LINKS

Table of n, a(n) for n=0..97.

MATHEMATICA

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-Fran├žois Alcover, Dec 11 2014 *)

CROSSREFS

Sequence in context: A032030 A184347 A006673 * A181264 A224766 A003181

Adjacent sequences:  A053975 A053976 A053977 * A053979 A053980 A053981

KEYWORD

cofr,nice,nonn

AUTHOR

Leroy Quet, Apr 02 2000

EXTENSIONS

More terms from Jeppe Stig Nielsen, Apr 13 2000

STATUS

approved

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Last modified August 1 07:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)