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-> denom(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_] := Denominator[ r[ hs[ Sort[ ContinuedFraction[ HarmonicNumber[n]]]]] ];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Mar 20 2017, after Alois P. Heinz *)
CROSSREFS
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