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Search: id:A084242
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| A084242 |
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Least k, 1<= k <=n, such that the number of elements of the continued fraction for n/k is maximum. |
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+0
6
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| 1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 11, 9, 10, 11, 11, 11, 13, 13, 14, 13, 14, 15, 17, 17, 18, 19, 18, 23, 19, 21, 22, 22, 23, 22, 25, 29, 23, 26, 25, 27, 26, 27, 29, 31, 30, 29, 28, 33, 33, 31, 34, 41, 32, 36, 33, 37, 33, 35, 37, 39, 47, 37, 41, 42, 40, 41, 41, 53, 45, 43
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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k>1, a(F(k))=F(k-1) where F(k) denotes the k-th Fibonacci number; probably, limit n ->oo 1/n*sum(k=1, n, a(k)) = 1/phi where phi is the Golden ratio (1+sqrt(5))/2
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PROGRAM
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(PARI) a(n)=if(n<0, 0, s=1; while(abs(vecmax(vector(n, i, length(contfrac(n/i))))-length(contfrac(n/s)))>0, s++); s)
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CROSSREFS
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Cf. A071677.
Sequence in context: A120835 A091374 A065603 this_sequence A156261 A071823 A139338
Adjacent sequences: A084239 A084240 A084241 this_sequence A084243 A084244 A084245
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 21 2003
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