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Search: id:A129084
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| A129084 |
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a(n) = numerator 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, 3, 7, 25, 88, 49, 219, 416, 4896, 4523, 68559, 40460, 613441, 791549, 487091, 1123701, 16678867, 4363873, 121113412, 24252821, 5893113, 7436454, 217867766, 306700798, 14495108003, 11420114688, 78503059517, 93975842393
(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-> numer (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, A129085.
Sequence in context: A148737 A148738 A148739 this_sequence A002870 A096579 A120540
Adjacent sequences: A129081 A129082 A129083 this_sequence A129085 A129086 A129087
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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 byond a(12) Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 04 2009
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