%I A109677
%S A109677 1,9,156,1696,3974,21558,82512,631294,5619414,93118405,739310894
%N A109677 a(1)=1; a(n) is the smallest integer > a(n-1) such that the largest element 
               in the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) 
               equals 3^n.
%e A109677 The continued fraction for S(5) = 1 + 1/9 + 1/156 + 1/1696 + 1/3974 is 
               [1, 8, 2, 4, 2, 1, 2, 1, 5, 4, 1, 3, 2, 243, 1, 1, 3] where the largest 
               element is 243=3^5 and 3974 is the smallest integer >1696 with this 
               property.
%t A109677 a[1] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1, s = Plus @@ (1/Table[a[i], 
               {i, n - 1}])}, While[Log[3, Max[ContinuedFraction[s + 1/k]]] != n, 
               k++ ]; k]; Do[ Print[ a[n]], {n, 11}] (from Robert G. Wilson v (rgwv(at)rgwv.com), 
               Aug 08 2005)
%o A109677 (PARI) s=1; t=1; for(n=2, 50, s=s+1/t; while(abs(3^n-vecmax(contfrac(s+1/
               t)))>0,t++); print1(t,","))
%Y A109677 Sequence in context: A045755 A009037 A012148 this_sequence A024122 A060348 
               A062232
%Y A109677 Adjacent sequences: A109674 A109675 A109676 this_sequence A109678 A109679 
               A109680
%K A109677 hard,nonn
%O A109677 1,2
%A A109677 Ryan Propper (rpropper(AT)stanford.edu), Aug 06 2005