A037842 -id:A037842 - cp's OEIS frontend

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

Hieronymus Fischer, Jun 26 2007

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

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

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

Cf. A000045, A061107.

Cf. A037842, A108047.

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

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

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

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

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.

A108047 Concatenation of the previous pair of numbers, with the first two terms both 1.

Original entry on oeis.org

1, 1, 11, 111, 11111, 11111111, 1111111111111, 111111111111111111111, 1111111111111111111111111111111111, 1111111111111111111111111111111111111111111111111111111, 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

Offset: 1

Parthasarathy Nambi, Jun 01 2005

The Fibonacci numbers, A000045, represented in base 1 (see A000042).

			The third term is 11 which is the concatenation of the first two terms 1 and 1.

Column b=1 of A214326.
Column k=1 of A214679.
Cf. A037842, A131293.

a(n) = (10^A000045(n)-1)/9.

a(n) = A000042(A000045(n)).

Edited by Jason Kimberley, Dec 15 2012

A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 11, 1, 1, 10, 111, 1, 1, 2, 11, 11111, 1, 1, 2, 10, 101, 11111111, 1, 1, 2, 3, 12, 1000, 1111111111111, 1, 1, 2, 3, 11, 22, 1101, 111111111111111111111, 1, 1, 2, 3, 10, 20, 111, 10101, 1111111111111111111111111111111111, 1, 1, 2, 3, 5, 13, 31, 210, 100010

Offset: 1

Alois P. Heinz, Jul 24 2012

For b > 10, some terms cannot be properly notated using only decimal characters.

			Square array A(n,b) begins:
              1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
              1,    1,   1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ...
             11,   10,   2,  2,  2,  2,  2,  2,  2,  2,  2,  2, ...
            111,   11,  10,  3,  3,  3,  3,  3,  3,  3,  3,  3, ...
          11111,  101,  12, 11, 10,  5,  5,  5,  5,  5,  5,  5, ...
       11111111, 1000,  22, 20, 13, 12, 11, 10,  8,  8,  8,  8, ...
  1111111111111, 1101, 111, 31, 23, 21, 16, 15, 14, 13, 12, 11, ...

Alois P. Heinz, Antidiagonals n = 1..13

Columns b=1-10, 12, 13 give: A108047, A004685, A004686, A004687, A004688, A004689, A004690, A004691, A004692, A000045, A004693, A004694.

Cf. A037842, A131293.

A:= proc(n, b) local f, l; f:= combinat[fibonacci](n);
      if b=1 then parse(cat(1$f))
    else l:= NULL;
         while f>0 do l:= irem(f, b, 'f'), l od;
         parse(cat(l))
      fi
    end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..10);

cp's OEIS Frontend

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.

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A108047 Concatenation of the previous pair of numbers, with the first two terms both 1.

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A214326 Square array read by antidiagonals in which T(n,b) gives the n-th Fibonacci number written in base b with n,b >= 1.

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Programs

Maple