login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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