%I #6 Feb 05 2014 20:18:06
%S 1,1,2,5,28,795,632167,399635138154,159708243647367169100509,
%T 25506723088926795724936617220833650734525459594,
%U 650592922735191299575059973922272937442761432150679274453311138653498403940208837571053997389
%N a(1) = 1; a(m) = maximum numerator possible with a continued fraction [b(1);b(2),b(3),...b(m-1)], where (b(1),b(2),b(3),...b(m-1)) is a permutation of (a(1),a(2),a(3),...a(m-1)).
%e a(5)=28 because the maximum numerator among permutations of (1,1,2,5)
%e happens when the continued fraction is [2;1,1,5]=28/11 or [5;1,1,2]=28/5.
%t a[1] = 1; a[n_] := a[n] = Union[ Numerator /@ FromContinuedFraction /@ Permutations[ Table[ a[i], {i, n - 1}]]] [[ -1]]; Table[ a[n], {n, 11}]
%Y Cf. A105788.
%K nonn
%O 1,3
%A _Leroy Quet_ and _Robert G. Wilson v_, Apr 19 2005