A121389 a(n) = 10^Fibonacci(n) - 1.

0, 9, 9, 99, 999, 99999, 99999999, 9999999999999, 999999999999999999999, 9999999999999999999999999999999999, 9999999999999999999999999999999999999999999999999999999

Offset

0,2

Comments

Each a(n) has Fibonacci(n) (trailing) 9's. In general, if the same recurrence below is used with any a(0), a(1) >= 0, then, for all k >= 2, a(k) has the same number of trailing 9's as a(k-2) and a(k-1) have altogether (see for example A121390).

Links

Table of n, a(n) for n=0..10.

Formula

a(n) = 10^Fibonacci(n) - 1 = 10^A000045(n) - 1 (= 9*A108047(n) for n>=1). a(0) = 0; a(1) = 9; a(n) = a(n-2)*a(n-1) + a(n-2) + a(n-1).

Mathematica

10^Fibonacci[Range[0, 10]]-1 (* Harvey P. Dale, Dec 24 2022 *)

Crossrefs

Cf. A000045, A063896, A108047, A121390.

Sequence in context: A050683 A210095 A092548 * A065242 A050720 A262860

Adjacent sequences: A121386 A121387 A121388 * A121390 A121391 A121392

Keyword

nonn

Author

Rick L. Shepherd, Jul 26 2006

Status

approved