The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081090 a(n)^2 + 1 = A081089(n), where A081089(n) = A081088(n+1)/A081088(n); involves the partial quotients of a series of continued fractions that sum to unity. 4
 0, 2, 5, 52, 13525, 9512132552, 1223751003414213892335125, 14245051228051734585272181044575005954679284643762013257552 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS log(a(n+1))/log(a(n)) -> 1+sqrt(2). The 8th term has 59 digits, while the 9th term has 141 digits. sum(n>0, a(n)/a(n+1) ) = 1/2; the ratio of the terms a(n+1)/a(n), for n>1, form the convergents of the continued fraction series described by A081088; thus a(n+1) = A081088(n)*a(n) + a(n-1), for n>1. - Paul D. Hanna, Mar 05 2003 LINKS Table of n, a(n) for n=1..8. FORMULA a(n) = a(n-2)*(a(n-1)^2 + 1) for n>3, with a(1)=0, a(2)=2, a(3)=5. Also, a(n)*a(n-1) = A081088(n) for n>2, a(n) = a(n-2)*A081089(n-1) for n>2. CROSSREFS Cf. A081086, A081088, A081089. Sequence in context: A216079 A206584 A268286 * A330282 A071880 A071882 Adjacent sequences: A081087 A081088 A081089 * A081091 A081092 A081093 KEYWORD nonn,easy AUTHOR Hans Havermann and Paul D. Hanna, Mar 05 2003 STATUS approved

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

Last modified June 17 15:40 EDT 2024. Contains 373458 sequences. (Running on oeis4.)