A131293 Concatenate a(n-2) and a(n-1) to get a(n); start with a(0)=0, a(1)=1, delete the leading zero. Also: concatenate Fibonacci(n) 1's.

0, 1, 1, 11, 111, 11111, 11111111, 1111111111111, 111111111111111111111, 1111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111

Offset: 0

Author

Hieronymus Fischer, Jun 26 2007

Keywords

• nonn
• base

Comments

Interpreted as base-2 numbers the result is A063896.

This sequence differs from A108047 by the leading a(0) = 0. - Jason Kimberley, Dec 15 2012

Examples

			a(3)=11, a(4)=111, so a(5) = a(4)*a(3) = 11111.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..18

Crossrefs

Cf. A000045, A061107.

Cf. A037842, A108047.

Programs

Haskell

import Data.Function (on)
a131293 n = a131293_list !! n
a131293_list = 0 : 1 : map read
               (zipWith ((++) `on` show) a131293_list $ tail a131293_list)
-- Reinhard Zumkeller, Oct 05 2015

Magma

[(10^Fibonacci(n)-1)/9: n in [0..10]]; // Vincenzo Librandi, Aug 29 2011

Maple

a:= n-> parse(cat(0, 1$combinat[fibonacci](n))):
seq(a(n), n=0..11);  # Alois P. Heinz, Apr 17 2020

Mathematica

Join[{0},FromDigits/@(PadLeft[{},#,1]&/@Fibonacci[Range[10]])] (* Harvey P. Dale, Aug 28 2011 *)

Formula

a(n) = a(n-2)*10^ceiling(log_10(a(n-1))) + a(n-1) for n > 1.

a(n) = (10^Fibonacci(n) - 1)/9.