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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 Fibonacci(n) - number of '1's. 5
0, 1, 1, 11, 111, 11111, 11111111, 1111111111111, 111111111111111111111, 1111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111 (list; graph; refs; listen; history; text; internal format)
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 Kimberly_, Dec 15 2012

LINKS

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

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.

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

Cf. A000045, A061107.

Cf. A037842, A108047.

Sequence in context: A117293 A015468 A037842 * A108047 A144784 A030175

Adjacent sequences:  A131290 A131291 A131292 * A131294 A131295 A131296

KEYWORD

nonn,base

AUTHOR

Hieronymus Fischer, Jun 26 2007

STATUS

approved

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Last modified October 16 23:30 EDT 2019. Contains 328103 sequences. (Running on oeis4.)