%I #11 Aug 09 2021 11:49:28
%S 1,3,1,3,27,49,768,536787,447787921,152366008416,
%T 1467260192414284896189483,42330538074919361326754372602670429768,
%U 23344669169302077506789751512287756127326423255355122538496
%N a(n) is the denominator of b(n): b(1)=2. b(n) be such that the continued fraction (of +-rational terms) [b(1); b(2), ..., b(n)] = Sum_{k=1..n-1} 1/b(k), for every integer n >= 2.
%C This sequence is infinite if and only if b(n) does not equal -b(n+1) for every positive integer n.
%H Jinyuan Wang, <a href="/A128777/b128777.txt">Table of n, a(n) for n = 1..18</a>
%F For n >= 5, b(n) = - (b(n-1) + b(n-2)) * (b(n-2) + b(n-3)) / (b(n-1) * b(n-2)^2).
%e {b(k)} begins: 2, -2/3, 3, 7/3, -16/27, 141/49, -3023/768, ...
%e So for example, 1/2 - 3/2 + 1/3 = 2 + 1/(-2/3 + 1/(3 + 3/7)) and 1/2 - 3/2 + 1/3 + 3/7 = 2 + 1/(-2/3 + 1/(3 + 1/(7/3 - 27/16))).
%o (PARI) lista(nn) = my(w, x=-2/3, y=3, z=7/3); print1("1, 3, 1, 3"); for(n=5, nn, print1(", ", denominator(w=-(y+z)*(x+y)/y^2/z)); x=y; y=z; z=w); \\ _Jinyuan Wang_, Aug 09 2021
%Y Cf. A128776.
%K nonn,frac
%O 1,2
%A _Leroy Quet_, Mar 27 2007
%E More terms from _Jinyuan Wang_, Aug 09 2021