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 A129084 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. 4
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..750 EXAMPLE 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. MAPLE 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);  # Alois P. Heinz, Aug 04 2009 MATHEMATICA r[l_] := Module[{lj, j}, For[lj = Infinity; j = Length[l], j >= 1, j--, lj = l[[j]] + 1/lj]; lj]; hs[l_] := Module[{ll, h, s, m}, ll = {}; h = Length[l]; s = 1; m = s; While[s <= h, ll = Append[ll, l[[m]]]; If[m == h, h--; m = s, s++; m = h ]]; ll]; a[n_] := Numerator[ r[ hs[ Sort[ ContinuedFraction[ HarmonicNumber[n]]]]]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 20 2017, after Alois P. Heinz *) CROSSREFS Cf. A129082, A129083, A129085. Sequence in context: A148737 A148738 A148739 * A287892 A002870 A096579 Adjacent sequences:  A129081 A129082 A129083 * A129085 A129086 A129087 KEYWORD frac,nonn AUTHOR Leroy Quet, Mar 28 2007 EXTENSIONS More terms from Diana L. Mecum, Jun 16 2007 Extended beyond a(12) Alois P. Heinz, Aug 04 2009 STATUS approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)