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A141822
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Maximum term in the continued fraction of A141821(n)/n.
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6
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2, 2, 3, 2, 5, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 4, 2, 3, 3, 3, 3, 2, 2, 4, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 3, 3, 2, 4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 5, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 4, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Consider the continued fraction [0;c1,c2,...,cm] of k/n, with k<n and gcd(k,n)=1. Let f(k,n) be the maximum of the ci. Then a(n) is the minimum value of f(k,n).
Zaremba conjectured that a(n)<=5, a bound that is attained for n in A195901. It appears that n=150 may be the largest integer with a(n)=5, while n=6234 may be the largest integer with a(n)=4.
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LINKS
| T. D. Noe, Table of n, a(n) for n=2..2000
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MATHEMATICA
| Table[c=ContinuedFraction[Select[Range[n-1], GCD[ #, n]==1&]/n]; Min[Max/@c], {n, 150}]
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CROSSREFS
| See A141821 for the least value of k for each n.
See A141832, A141833, A141823, and A195901 for the integers n>1 such that a(n) = 2, 3, 4, and 5, respectively.
Sequence in context: A102247 A054249 A160273 * A033099 A018892 A100565
Adjacent sequences: A141819 A141820 A141821 * A141823 A141824 A141825
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jul 08 2008
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EXTENSIONS
| Edited by Max Alekseyev (maxale(AT)gmail.com), Sep 25 2011
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