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Search: id:A129085
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| A129085 |
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a(n) = denominator of b(n): b(n) = the minimum possible value for a continued fraction whose terms are a permutation of the terms of the simple continued fraction for H(n) = sum{k=1 to n} 1/k, the n-th harmonic number. |
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+0
4
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| 1, 2, 6, 12, 79, 22, 187, 369, 4343, 4220, 67223, 38067, 535331, 772210, 476254, 1020589, 15631362, 4294584, 116606407, 22970156, 5737508, 6936929, 185961619, 290508289, 13765708850, 10898842249, 77379962122, 91973292918
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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The continued fraction for H(5) = 137/60 is [2;3,1,1,8]. The minimum value a continued fraction can have with these same terms in some order is [1;8,1,3,2] = 88/79.
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MAPLE
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Contribution from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009: (Start)
with (numtheory): H:= proc(n) option remember; `if` (n=1, 1, H(n-1)+1/n) end:
r:= proc(l) local j; infinity; for j from nops(l) to 1 by -1 do l[j]+1/% od end:
hs:= proc(l) local ll, h, s, m; ll:= []; h:= nops(l); s:= 1; m:= s; while s<=h do ll:= [ll[], l[m]]; if m=h then h:= h-1; m:= s else s:= s+1; m:= h fi od; ll end:
a:= n-> denom (r (hs (sort (cfrac (H(n), 'quotients'))))): seq (a(n), n=1..40); (End)
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CROSSREFS
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Cf. A129082, A129083, A129084.
Sequence in context: A107763 A166470 A144144 this_sequence A141288 A062954 A038787
Adjacent sequences: A129082 A129083 A129084 this_sequence A129086 A129087 A129088
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet Mar 28 2007
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EXTENSIONS
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More terms from Diana Mecum (diana.mecum(AT)gmail.com), Jun 16 2007
Extended beyond a(12) Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009
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