Suite de Fibonacci

par **haiethem** Mer 12 Jan - 9:14

Definition[edit]

Let { S_{0}} $Suite de Fibonacci Ebe0ac45a38c4437bd2689a14ec434cd499e7e49$ be "0" and {S_{1}} $Suite de Fibonacci 5bf84e7fd4fb8259a9b37f956afdf83ee2a020f9$ be "01". Now {S_{n}=S_{n-1}S_{n-2}} $Suite de Fibonacci 16aa5fddafa83024168eb48d30f9b02fc1682592$ (the concatenation of the previous sequence and the one before that).
The infinite Fibonacci word is the limit {S_{}} $Suite de Fibonacci Ebfe462c3a7f2183faf705c10fc311580d11c49d$ , that is, the (unique) infinite sequence that contains each {S_{n}} $Suite de Fibonacci 9f049ac28d4ac8097b625f9d71c1f22b2ebd1bc4$ , for finite {n} $Suite de Fibonacci A601995d55609f2d9f5e233e36fbe9ea26011b3b$ , as a prefix.
Enumerating items from the above definition produces:
{S_{0}} $Suite de Fibonacci Ebe0ac45a38c4437bd2689a14ec434cd499e7e49$     0
{S_{1}} $Suite de Fibonacci 5bf84e7fd4fb8259a9b37f956afdf83ee2a020f9$     01
{S_{2}} $Suite de Fibonacci 1143e284d5f25cef778ab482edf6617a523ddd9f$     010
{S_{3}} $Suite de Fibonacci 70e15f3e200aaa247f69c43110cc5a09ecc91b89$     01001
{S_{4}} $Suite de Fibonacci Fc1632bc1d95d33ccb5473b9d8cc333c2dd0d13a$     01001010
{S_{5}} $Suite de Fibonacci 7d113353a42f71fc5e7154ddef2257079ab2e25a$     0100101001001
...
The first few elements of the infinite Fibonacci word are:
0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, ... (sequence A003849 in the OEIS)

par **haiethem** Sam 28 Jan - 11:34

ddezd

Suite de Fibonacci

Suite de Fibonacci

Definition[edit]

Re: Suite de Fibonacci