A128777 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.

1, 3, 1, 3, 27, 49, 768, 536787, 447787921, 152366008416, 1467260192414284896189483, 42330538074919361326754372602670429768, 23344669169302077506789751512287756127326423255355122538496

Offset

1,2

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("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

Crossrefs

Cf. A128776.

Sequence in context: A160708 A040173 A320952 * A286892 A215828 A067009

Adjacent sequences: A128774 A128775 A128776 * A128778 A128779 A128780

Keyword

nonn,frac

Author

Leroy Quet, Mar 27 2007

Extensions

More terms from Jinyuan Wang, Aug 09 2021

Status

approved