系列 1、11、55、239、991、…。
原文:https://www . geesforgeks . org/n-th-系列术语-1-11-55-239-991/
给定一个数字 N，任务是编写一个程序来寻找数列中的第 N 项:
1，11，55，239，991，…
示例 :
Input: N = 3
Output: 55
Input: N = 4
Output: 239
方法-1: 写下给定数字的二进制表示时，可以观察到一种模式。
1 = 1 11 = 1011 55 = 110111 239 = 11101111 。 。 。
因此，对于 N = 1，答案永远是 1。对于第 N 项，二进制字符串将是 (n-1)1 + (0) + (n)1 ，其被转换为十进制值以获得答案。 以下是上述方法的实施:
C++
// C++ program to find the N-th term
// in 1, 11, 55, 239, 991, ....
#include <bits/stdc++.h>
using namespace std;
// Function to return the decimal value
// of a binary number
int binaryToDecimal(string n)
{
string num = n;
int dec_value = 0;
// Initializing base value to 1, i.e 2^0
int base = 1;
int len = num.length();
for (int i = len - 1; i >= 0; i--) {
if (num[i] == '1')
dec_value += base;
base = base * 2;
}
return dec_value;
}
// find the binary representation
// of the N-th number in sequence
int numberSequence(int n)
{
// base case
if (n == 1)
return 1;
// answer string
string s = "";
// add n-1 1's
for (int i = 1; i < n; i++)
s += '1';
// add 0
s += '0';
// add n 1's at end
for (int i = 1; i <= n; i++)
s += '1';
int num = binaryToDecimal(s);
return num;
}
// Driver Code
int main()
{
int n = 4;
cout << numberSequence(n);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the N-th
// term in 1, 11, 55, 239, 991, ....
import java.util.*;
class GFG
{
// Function to return the decimal
// value of a binary number
static int binaryToDecimal(String n)
{
String num = n;
int dec_value = 0;
// Initializing base
// value to 1, i.e 2^0
int base = 1;
int len = num.length();
for (int i = len - 1; i >= 0; i--)
{
if (num.charAt(i) == '1')
dec_value += base;
base = base * 2;
}
return dec_value;
}
// find the binary representation
// of the N-th number in sequence
static int numberSequence(int n)
{
// base case
if (n == 1)
return 1;
// answer string
String s = "";
// add n-1 1's
for (int i = 1; i < n; i++)
s += '1';
// add 0
s += '0';
// add n 1's at end
for (int i = 1; i <= n; i++)
s += '1';
int num = binaryToDecimal(s);
return num;
}
// Driver Code
public static void main(String args[])
{
int n = 4;
System.out.println(numberSequence(n));
}
}
// This code is contributed
// by Arnab Kundu
Python 3
# Python 3 program to find the N-th term
# in 1, 11, 55, 239, 991, ....
# Function to return the decimal value
# of a binary number
def binaryToDecimal(n):
num = n
dec_value = 0
# Initializing base value to 1, i.e 2^0
base = 1
l = len(num)
for i in range(l - 1,-1, -1):
if (num[i] == '1'):
dec_value += base
base = base * 2
return dec_value
# find the binary representation
# of the N-th number in sequence
def numberSequence(n):
# base case
if (n == 1):
return 1
# answer string
s = ""
# add n-1 1's
for i in range(1, n):
s += '1'
# add 0
s += '0'
# add n 1's at end
for i in range(1,n+1):
s += '1'
num = binaryToDecimal(s)
return num
# Driver Code
if __name__ == "__main__":
n = 4
print(numberSequence(n))
# this code is contributed by ChitraNayal
C
// C# program to find the N-th
// term in 1, 11, 55, 239, 991, ....
using System;
class GFG
{
// Function to return the decimal
// value of a binary number
static int binaryToDecimal(String n)
{
String num = n;
int dec_value = 0;
// Initializing base
// value to 1, i.e 2^0
int base_ = 1;
int len = num.Length;
for (int i = len - 1; i >= 0; i--)
{
if (num[i] == '1')
dec_value += base_;
base_ = base_ * 2;
}
return dec_value;
}
// find the binary representation
// of the N-th number in sequence
static int numberSequence(int n)
{
// base case
if (n == 1)
return 1;
// answer string
String s = "";
// add n-1 1's
for (int i = 1; i < n; i++)
s += '1';
// add 0
s += '0';
// add n 1's at end
for (int i = 1; i <= n; i++)
s += '1';
int num = binaryToDecimal(s);
return num;
}
// Driver Code
public static void Main()
{
int n = 4;
Console.WriteLine(numberSequence(n));
}
}
// This code is contributed
// by Subhadeep
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find the N-th term
// in 1, 11, 55, 239, 991, ....
// Function to return the decimal
// value of a binary number
function binaryToDecimal($n)
{
$num = $n;
$dec_value = 0;
// Initializing base value
// to 1, i.e 2^0
$base = 1;
$len = strlen($num);
for ($i = $len - 1; $i >= 0; $i--)
{
if ($num[$i] == '1')
$dec_value += $base;
$base = $base * 2;
}
return $dec_value;
}
// find the binary representation
// of the N-th number in sequence
function numberSequence($n)
{
// base case
if ($n == 1)
return 1;
// answer string
$s = "";
// add n-1 1's
for ($i = 1; $i < $n; $i++)
$s .= '1';
// add 0
$s .= '0';
// add n 1's at end
for ($i = 1; $i <= $n; $i++)
$s .= '1';
$num = binaryToDecimal($s);
return $num;
}
// Driver Code
$n = 4;
echo numberSequence($n);
// This code is contributed by mits
?>
java 描述语言
<script>
// Javascript program to find the N-th term
// in 1, 11, 55, 239, 991, ....
// Function to return the decimal value
// of a binary number
function binaryToDecimal(n)
{
let num = n;
let dec_value = 0;
// Initializing base value to 1, i.e 2^0
let base = 1;
let len = num.length;
for (let i = len - 1; i >= 0; i--) {
if (num[i] == '1')
dec_value += base;
base = base * 2;
}
return dec_value;
}
// find the binary representation
// of the N-th number in sequence
function numberSequence(n)
{
// base case
if (n == 1)
return 1;
// answer string
let s = "";
// add n-1 1's
for (let i = 1; i < n; i++)
s += '1';
// add 0
s += '0';
// add n 1's at end
for (let i = 1; i <= n; i++)
s += '1';
let num = binaryToDecimal(s);
return num;
}
// Driver Code
let n = 4;
document.write(numberSequence(n));
// This code is contributed by subhammahato348.
</script>
Output:
239
逼近-2: 级数有一个通式 4 N -2 N -1 ，用来得到级数的第 N 项。 以下是上述方法的实施:
C++
// C++ program to find the N-th term
// in 1, 11, 55, 239, 991, ....
#include <bits/stdc++.h>
using namespace std;
// Function to find the N-th term
int numberSequence(int n)
{
// calculates the N-th term
int num = pow(4, n) - pow(2, n) - 1;
return num;
}
// Driver Code
int main()
{
int n = 4;
cout << numberSequence(n);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to find the N-th
// term in 1, 11, 55, 239, 991, ....
class GFG
{
// Function to find the N-th term
static int numberSequence(int n)
{
// calculates the N-th term
int num = (int)(Math.pow(4, n) -
Math.pow(2, n)) - 1;
return num;
}
// Driver Code
public static void main(String args[])
{
int n = 4;
System.out.println(numberSequence(n));
}
}
// This code is contributed
// by Arnab Kundu
Python 3
# Python 3 program to find N-th term
# in 1, 11, 55, 239, 991, ....
# calculate Nth term of series
def numberSequence(n) :
# calculates the N-th term
num = pow(4, n) - pow(2, n) - 1
return num
# Driver Code
if __name__ == "__main__" :
n = 4
print(numberSequence(n))
# This code is contributed by ANKITRAI1
C
// C# program to find the N-th
// term in 1, 11, 55, 239, 991, ....
using System;
class GFG
{
// Function to find the N-th term
static int numberSequence(int n)
{
// calculates the N-th term
int num = (int)(Math.Pow(4, n) -
Math.Pow(2, n)) - 1;
return num;
}
// Driver Code
public static void Main()
{
int n = 4;
Console.WriteLine(numberSequence(n));
}
}
// This code is contributed
// by chandan_jnu.
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?php
// PHP program to find the N-th term
// in 1, 11, 55, 239, 991, ....
// Function to find the N-th term
function numberSequence($n)
{
// calculates the N-th term
$num = pow(4, $n) -
pow(2, $n) - 1;
return $num;
}
// Driver Code
$n = 4;
echo numberSequence($n);
// This code is contributed by mits
?>
java 描述语言
<script>
// Javascript program to find the N-th term
// in 1, 11, 55, 239, 991, ....
// Function to find the N-th term
function numberSequence(n)
{
// calculates the N-th term
let num = Math.pow(4, n) - Math.pow(2, n) - 1;
return num;
}
// Driver Code
let n = 4;
document.write(numberSequence(n));
</script>
Output:
239
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