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Search: id:A141822
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| A141822 |
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Maximum value of a term in the continued fraction of A141821(n)/n. |
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+0
5
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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; listen)
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OFFSET
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2,1
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COMMENT
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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=6,54,150. It appears that n=6234 may be the last number with a(n)=4. See A141821 for the least value of k for each n. See A141823 for the n such that a(n)=4.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..2000
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MATHEMATICA
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Table[c=ContinuedFraction[Select[Range[n-1], GCD[ #, n]==1&]/n]; Min[Max/@c], {n, 150}]
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CROSSREFS
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Sequence in context: A102247 A054249 A160273 this_sequence A033099 A018892 A100565
Adjacent sequences: A141819 A141820 A141821 this_sequence A141823 A141824 A141825
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 08 2008
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