Secuencia Stern-Brocot

La secuencia de Stern Brocot es similar a la secuencia de Fibonacci pero es diferente en la forma en que se genera la secuencia de Fibonacci. 
Generación de la secuencia Stern Brocot:
 

1. El primer y segundo elemento de la secuencia son 1 y 1.
2. Considere el segundo miembro de la secuencia. Luego, suma el miembro considerado de la secuencia y su precedente, es decir (1 + 1 = 2). Ahora 2 es el siguiente elemento de nuestra serie. La secuencia será [ 1, 1, 2 ]
3. Después de este elemento, nuestro próximo elemento de la secuencia será el elemento considerado de nuestro segundo paso. Ahora la secuencia será [ 1, 1, 2, 1 ]
4. Nuevamente hacemos el paso 2, pero ahora el elemento considerado será el 2 (3er elemento). Entonces, el próximo número de secuencia será la suma del número considerado y su precedente (2 + 1 = 3). La secuencia será ahora [1, 1, 2, 1, 3]
5. Al igual que el paso 3, el siguiente elemento será el elemento considerado, es decir, 2. Por lo tanto, la secuencia será [ 1, 1, 2, 1, 3, 2 ]
6. Por lo tanto, este proceso continúa, ahora el siguiente elemento considerado será 1 (4º elemento). 
 

Aquí está el programa simple para imprimir la secuencia Stern Brocot. 
 

// CPP program to print Brocot Sequence
#include <bits/stdc++.h>
using namespace std;
 
void SternSequenceFunc(vector<int>& BrocotSequence, int n)
{
    // loop to create sequence
    for (int i = 1; BrocotSequence.size() < n; i++)
    {
        int considered_element = BrocotSequence[i];
        int precedent = BrocotSequence[i - 1];
 
        // adding sum of considered element and it's precedent
        BrocotSequence.push_back(considered_element + precedent);
         
        // adding next considered element
        BrocotSequence.push_back(considered_element);
    }
 
    // printing sequence..
    for (int i = 0; i < 15; ++i)
        cout << BrocotSequence[i] << " ";
}
 
int main()
{
    int n = 15;
    vector<int> BrocotSequence;
     
    // adding first two element
    // in the sequence
    BrocotSequence.push_back(1);
    BrocotSequence.push_back(1);
     
    SternSequenceFunc(BrocotSequence, n);
 
    return 0;
}

// Java program to print
// Brocot Sequence
import java.io.*;
import java.util.*;
 
class GFG {
     
static void SternSequenceFunc(Vector<Integer>
                         BrocotSequence, int n)
{
    // loop to create sequence
    for (int i = 1; BrocotSequence.size() < n; i++)
    {
        int considered_element = BrocotSequence.get(i);
        int precedent = BrocotSequence.get(i-1);
 
        // adding sum of considered element and it's precedent
        BrocotSequence.add(considered_element + precedent);
         
        // adding next considered element
        BrocotSequence.add(considered_element);
    }
 
    // printing sequence..
    for (int i = 0; i < 15; ++i)
        System.out.print(BrocotSequence.get(i) + " ");
}
    // Driver code
    public static void main (String[] args) {
         
        int n = 15;
        Vector<Integer> BrocotSequence = new Vector<Integer>();
         
        // adding first two element
        // in the sequence
        BrocotSequence.add(1);
        BrocotSequence.add(1);
         
        SternSequenceFunc(BrocotSequence, n);
         
    }
}
 
// This code is contributed by Gitanjali.

# Python program to print
# Brocot Sequence
import math
  
def SternSequenceFunc(BrocotSequence, n):
     
    # loop to create sequence
    for i in range(1,  n):
         
        considered_element = BrocotSequence[i]
        precedent = BrocotSequence[i-1]
  
        # adding sum of considered
        # element and it's precedent
        BrocotSequence.append(considered_element + precedent)
          
        # adding next considered element
        BrocotSequence.append(considered_element)
     
  
    # printing sequence..
    for i in range(0, 15):
        print(BrocotSequence[i] , end=" ")
 
# Driver code
n = 15
BrocotSequence = []
 
# adding first two element
# in the sequence
BrocotSequence.append(1)
BrocotSequence.append(1)
          
SternSequenceFunc(BrocotSequence, n)
 
# This code is contributed by Gitanjali.

// C# program to print
// Brocot Sequence
using System;
using System.Collections.Generic;
 
class GFG
{
static void SternSequenceFunc(List<int>
                 BrocotSequence, int n)
{
    // loop to create sequence
    for (int i = 1;
             BrocotSequence.Count < n; i++)
    {
        int considered_element =
                       BrocotSequence[i];
        int precedent =
                   BrocotSequence[i - 1];
 
        // adding sum of considered
        // element and it's precedent
        BrocotSequence.Add(considered_element +
                                    precedent);
         
        // adding next
        // considered element
        BrocotSequence.Add(
                       considered_element);
    }
 
    // printing sequence..
    for (int i = 0; i < 15; ++i)
        Console.Write(
                BrocotSequence[i] + " ");
}
// Driver code
static void Main ()
{
     
    int n = 15;
    List<int> BrocotSequence =
                    new List<int>();
     
    // adding first two element
    // in the sequence
    BrocotSequence.Add(1);
    BrocotSequence.Add(1);
     
    SternSequenceFunc(BrocotSequence, n);
}
}
 
// This code is contributed by
// Manish Shaw(manishshaw1)

<?php
// PHP program to
// print Brocot Sequence
 
function SternSequenceFunc(&$BrocotSequence, $n)
{
    // loop to create sequence
    for ($i = 1;
         count($BrocotSequence) < $n;
         $i++)
    {
        $considered_element =
                    $BrocotSequence[$i];
        $precedent = $BrocotSequence[$i - 1];
 
        // adding sum of considered
        // element and it's precedent
        array_push($BrocotSequence,
                   $considered_element +
                   $precedent);
         
        // adding next
        // considered element
        array_push($BrocotSequence,
                   $considered_element);
    }
     
    // printing sequence..
    for ($i = 0; $i < 15; ++$i)
        echo ($BrocotSequence[$i]." ");
}
 
// Driver code
$n = 15;
$BrocotSequence = array();
 
// adding first two element
// in the sequence
array_push($BrocotSequence, 1);
array_push($BrocotSequence, 1);
 
SternSequenceFunc($BrocotSequence, $n);
 
// This code is contributed by
// Manish Shaw(manishshaw1)
?>

<script>
 
// Javascript program to print Brocot Sequence
 
function SternSequenceFunc( BrocotSequence, n)
{
    // loop to create sequence
    for (var i = 1; BrocotSequence.length < n; i++)
    {
        var considered_element = BrocotSequence[i];
        var precedent = BrocotSequence[i - 1];
 
        // adding sum of considered element and it's precedent
        BrocotSequence.push(considered_element + precedent);
         
        // adding next considered element
        BrocotSequence.push(considered_element);
    }
 
    // printing sequence..
    for (var i = 0; i < 15; ++i)
        document.write( BrocotSequence[i] + " ");
}
 
var n = 15;
var BrocotSequence = [];
 
// adding first two element
// in the sequence
BrocotSequence.push(1);
BrocotSequence.push(1);
 
SternSequenceFunc(BrocotSequence, n);
 
// This code is contributed by rrrtnx.
</script>

Producción: 
 

1 1 2 1 3 2 3 1 4 3 5 2 5 3 4

Referencias:  
Github