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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.
7
0, 1, 1, 11, 111, 11111, 11111111, 1111111111111, 111111111111111111111, 1111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111
OFFSET
0,4
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
LINKS
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.
EXAMPLE
a(3)=11, a(4)=111, so a(5) = a(4)*a(3) = 11111.
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 *)
PROG
(Magma) [(10^Fibonacci(n)-1)/9: n in [0..10]]; // Vincenzo Librandi, Aug 29 2011
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Hieronymus Fischer, Jun 26 2007
STATUS
approved