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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-Fran├žois 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 February 17 15:19 EST 2019. Contains 320220 sequences. (Running on oeis4.)