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 A128776 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. 2
 2, -2, 3, 7, -16, 141, -3023, -39839, 1653303453, 108704047205099, -391426132400729133357016, 159437481180981455205331487375079127161, -217366990514548285399449172911200019767497559051174761209795475 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence is infinite if and only if b(n) does not equal -b(n+1) for every positive integer n. LINKS Jinyuan Wang, Table of n, a(n) for n = 1..18 FORMULA For n >= 5, b(n) = - (b(n-1) + b(n-2)) * (b(n-2) + b(n-3)) / (b(n-1) * b(n-2)^2). EXAMPLE {b(k)} begins: 2, -2/3, 3, 7/3, -16/27, 141/49, -3023/768, ... 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))). PROG (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 CROSSREFS Cf. A128777. Sequence in context: A032257 A038075 A032236 * A117387 A113842 A032161 Adjacent sequences:  A128773 A128774 A128775 * A128777 A128778 A128779 KEYWORD sign,frac AUTHOR Leroy Quet, Mar 27 2007 EXTENSIONS More terms from Jinyuan Wang, Aug 09 2021 STATUS approved

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Last modified September 23 19:03 EDT 2021. Contains 347617 sequences. (Running on oeis4.)