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Search: id:A109677
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| A109677 |
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a(1)=1; a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals 3^n. |
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1
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| 1, 9, 156, 1696, 3974, 21558, 82512, 631294, 5619414, 93118405, 739310894
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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The continued fraction for S(5) = 1 + 1/9 + 1/156 + 1/1696 + 1/3974 is [1, 8, 2, 4, 2, 1, 2, 1, 5, 4, 1, 3, 2, 243, 1, 1, 3] where the largest element is 243=3^5 and 3974 is the smallest integer >1696 with this property.
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1, s = Plus @@ (1/Table[a[i], {i, n - 1}])}, While[Log[3, Max[ContinuedFraction[s + 1/k]]] != n, k++ ]; k]; Do[ Print[ a[n]], {n, 11}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Aug 08 2005)
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PROGRAM
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(PARI) s=1; t=1; for(n=2, 50, s=s+1/t; while(abs(3^n-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))
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CROSSREFS
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Adjacent sequences: A109674 A109675 A109676 this_sequence A109678 A109679 A109680
Sequence in context: A113137 A009037 A012148 this_sequence A024122 A060348 A062232
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KEYWORD
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hard,nonn
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AUTHOR
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Ryan Propper (rpropper(AT)stanford.edu), Aug 06 2005
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