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%I #11 Aug 09 2021 11:49:34
%S 2,-2,3,7,-16,141,-3023,-39839,1653303453,108704047205099,
%T -391426132400729133357016,159437481180981455205331487375079127161,
%U -217366990514548285399449172911200019767497559051174761209795475
%N a(n) is the numerator 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="/A128776/b128776.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("2, -2, 3, 7"); for(n=5, nn, print1(", ", numerator(w=-(y+z)*(x+y)/y^2/z)); x=y; y=z; z=w); \\ _Jinyuan Wang_, Aug 09 2021
%Y Cf. A128777.
%K sign,frac
%O 1,1
%A _Leroy Quet_, Mar 27 2007
%E More terms from _Jinyuan Wang_, Aug 09 2021
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