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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086695 a(n) = 100^n - 10^n - 1. 1
 89, 9899, 998999, 99989999, 9999899999, 999998999999, 99999989999999, 9999999899999999, 999999998999999999, 99999999989999999999, 9999999999899999999999, 999999999998999999999999, 99999999999989999999999999, 9999999999999899999999999999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Digits of the inverses of these numbers give the Fibonacci numbers. More precisely, the digits of 1/(10^(2*n)-10^n-1) give the Fibonacci numbers up to 10^n. More generally, if x_1, x_2, x_n=x_(n-1)-x_(n-2) is any Lucas sequence, then the digits of the numbers (x_1*10^n-(x_1-x_2))/(10^(2*n)-10^n-1) give the x_n up to 10^n. 1/a(n) = Sum_{i>=1) A000045(i-1)/10^(n*i) (see Long paper). - Michel Marcus, May 01 2013 LINKS C. T. Long, The Decimal Expansion of 1/89 and Related Results, The Fibonacci Quarterly, Volume 19, Number 1, February 1981 Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000). FORMULA a(n) = 10^(2*n) - 10^n - 1. PROG (PARI) a(n)=100^n-10^n-1 \\ Charles R Greathouse IV, May 01 2013 CROSSREFS Sequence in context: A263431 A093948 A116254 * A056568 A174758 A181681 Adjacent sequences:  A086692 A086693 A086694 * A086696 A086697 A086698 KEYWORD easy,nonn AUTHOR Maurice Mischler (maurice.mischler(AT)ima.unil.ch), Sep 12 2003 EXTENSIONS Offset corrected by Jon E. Schoenfield, Jun 17 2018 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.

Last modified October 21 18:05 EDT 2020. Contains 337919 sequences. (Running on oeis4.)