# Digit – Product – Sequence

Given a number N, the task is to print the sequence upto N. The sequence is : 1, 2, 4, 8, 16, 22, 26, 38, 62, 74, 102, 104, 108, 116, 122, 126, 138, 162 and so on… This sequence is known as Digit – Product – Sequence. In this series, we take every non zero digit of the number, multiply them and add the product to the number itself.

Examples:

```Input : N = 10
Output :1 2 4 8 16 22 26 38 62 74

Input : N = 7
Output :1 2 4 8 16 22 26
```

Explanation:

```1 + (1 * 1)  = 1 + 1  = 2
2 + (2 * 1)  = 2 + 2  = 4
4 + (4 * 1)  = 4 + 4  = 8
8 + (8 * 1)  = 8 + 8  = 16
16 + (1 * 6) = 16 + 6 = 22
22 + (2 * 2) = 22 + 4 = 26
26 + (2 * 6) = 26 + 12 = 38
38 + (3 * 8) = 38 + 24 = 62
62 + (6 * 2) = 62 + 12 = 74
and so on...
```

## C++

 `// CPP program for Digit Product Sequence ` `#include ` `using` `namespace` `std; ` ` `  `// function to produce and print Digit ` `// Product Sequence ` `void` `digit_product_Sum(``int` `N) ` `{ ` `    ``// Array which store sequence ` `    ``int` `a[N]; ` ` `  `    ``// Temporary variable to store product ` `    ``int` `product = 1; ` ` `  `    ``// Initialize first element of the  ` `    ``// array with 1 ` `    ``a = 1; ` ` `  `    ``// Run a loop from 1 to N. Check if  ` `    ``// previous number is single digit or ` `    ``// not. If yes then product = 1 else ` `    ``// take modulus. Then again check if  ` `    ``// previous number is sigle digit or  ` `    ``// not if yes then store previous number, ` `    ``// else store its first value Then for ` `    ``// every i store value in the array. ` `    ``for` `(``int` `i = 1; i <= N; i++) { ` `        ``product = a[i - 1] / 10; ` `     `  `        ``if` `(product == 0) ` `            ``product = 1; ` `        ``else` `            ``product = a[i - 1] % 10; ` `     `  `        ``int` `val = a[i - 1] / 10; ` `     `  `        ``if` `(val == 0) ` `            ``val = a[i - 1]; ` `     `  `        ``a[i] = a[i - 1] + (val * product); ` `    ``} ` ` `  `    ``// Print sequence ` `    ``for` `(``int` `i = 0; i < N; i++) ` `        ``cout << a[i] << ``" "``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Value of N ` `    ``int` `N = 10; ` ` `  `    ``// Calling function ` `    ``digit_product_Sum(N); ` `    ``return` `0; ` `} `

## Java

 `// Java program for Digit Product Sequence ` ` `  `// function to produce and print Digit ` `// Product Sequence ` `import` `java.lang.*; ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` `    ``public` `static` `void` `digit_product_Sum(``int` `N) ` `    ``{ ` `        ``// Array which store sequence ` `        ``int` `a[] = ``new` `int``[N+``1``] ; ` ` `  `        ``// Temporary variable to store product ` `        ``int` `product = ``1``; ` ` `  `        ``// Initialize first element of the ` `        ``// array with 1 ` `        ``a[``0``] = ``1``; ` ` `  `        ``// Run a loop from 1 to N. Check if ` `        ``// previous number is single digit or ` `        ``// not. If yes then product = 1 else ` `        ``// take modulus. Then again check if ` `        ``// previous number is sigle digit or ` `        ``// not if yes then store previous number, ` `        ``// else store its first value Then for ` `        ``// every i store value in the array. ` `        ``for` `(``int` `i = ``1``; i <= N; i++) ` `        ``{ ` `            ``product = a[i - ``1``] / ``10``; ` ` `  `            ``if` `(product == ``0``) ` `                ``product = ``1``; ` `            ``else` `                ``product = a[i - ``1``] % ``10``; ` ` `  `            ``int` `val = a[i - ``1``] / ``10``; ` ` `  `            ``if` `(val == ``0``) ` `                ``val = a[i - ``1``]; ` ` `  `            ``a[i] = a[i - ``1``] + (val * product); ` `        ``} ` ` `  `        ``// Print sequence ` `        ``for` `(``int` `i = ``0``; i < N; i++) ` `            ``System.out.print(a[i] + ``" "``); ` `    ``} ` ` `  `// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``// Value of N ` `        ``int` `N = ``10``; ` ` `  `        ``// Calling function ` `        ``digit_product_Sum(N); ` ` `  `    ``} ` `} ` `// Code contributed by Mohit Gupta_OMG <(0_o)> `

## Python3

 `# Python3 program for  ` `# Digit Product Sequence ` ` `  `# function to produce and  ` `# print Digit Product Sequence ` ` `  `def` `digit_product_Sum(N): ` `     `  `    ``# Array which store sequence ` `    ``a ``=` `[``0``] ``*` `(N ``+` `1``); ` `     `  `    ``# Temporary variable ` `    ``# to store product ` `    ``product ``=` `1``; ` `     `  `    ``# Initialize first element  ` `    ``# of the array with 1 ` `    ``a[``0``] ``=` `1``; ` `     `  `    ``# Run a loop from 1 to N.  ` `    ``# Check if previous number  ` `    ``# is single digit or not.  ` `    ``# If yes then product = 1  ` `    ``# else take modulus. Then  ` `    ``# again check if previous  ` `    ``# number is sigle digit or ` `    ``# not if yes then store  ` `    ``# previous number, else store  ` `    ``# its first value Then for ` `    ``# every i store value in  ` `    ``# the array. ` `    ``for` `i ``in` `range``(``1``, N ``+` `1``): ` `        ``product ``=` `int``(a[i ``-` `1``] ``/` `10``); ` `        ``if` `(product ``=``=` `0``): ` `            ``product ``=` `1``; ` `        ``else``: ` `            ``product ``=` `a[i ``-` `1``] ``%` `10``; ` `         `  `        ``val ``=` `int``(a[i ``-` `1``] ``/` `10``); ` `        ``if` `(val ``=``=` `0``): ` `            ``val ``=` `a[i ``-` `1``]; ` `        ``a[i] ``=` `a[i ``-` `1``] ``+` `(val ``*` `product); ` `     `  `    ``# Print sequence ` `    ``for` `i ``in` `range``(N): ` `        ``print``(a[i], end ``=` `" "``); ` `         `  `# Driver Code ` ` `  `# Value of N ` `N ``=` `10``; ` ` `  `# Calling function ` `digit_product_Sum(N); ` ` `  `# This Code is contributed ` `# by mits. `

## C#

 `// C# program for Digit Product Sequence ` `// function to produce and print Digit ` `// Product Sequence ` `using` `System; ` ` `  `class` `GFG ` `{ ` `    ``public` `static` `void` `digit_product_Sum(``int` `N) ` `    ``{ ` `        ``// Array which store sequence ` `        ``int` `[]a = ``new` `int``[N + 1] ; ` ` `  `        ``// Temporary variable to store product ` `        ``int` `product = 1; ` ` `  `        ``// Initialize first element of the ` `        ``// array with 1 ` `        ``a = 1; ` ` `  `        ``// Run a loop from 1 to N. Check if ` `        ``// previous number is single digit or ` `        ``// not. If yes then product = 1 else ` `        ``// take modulus. Then again check if ` `        ``// previous number is sigle digit or ` `        ``// not if yes then store previous number, ` `        ``// else store its first value Then for ` `        ``// every i store value in the array. ` `        ``for` `(``int` `i = 1; i <= N; i++) ` `        ``{ ` `            ``product = a[i - 1] / 10; ` ` `  `            ``if` `(product == 0) ` `                ``product = 1; ` `            ``else` `                ``product = a[i - 1] % 10; ` ` `  `            ``int` `val = a[i - 1] / 10; ` ` `  `            ``if` `(val == 0) ` `                ``val = a[i - 1]; ` ` `  `            ``a[i] = a[i - 1] + (val * product); ` `        ``} ` ` `  `        ``// Print sequence ` `        ``for` `(``int` `i = 0; i < N; i++) ` `        ``Console.Write(a[i] + ``" "``); ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``// Value of N ` `        ``int` `N = 10; ` ` `  `        ``// Calling function ` `        ``digit_product_Sum(N); ` ` `  `    ``} ` `} ` `// This Code is contributed by vt_m. `

## PHP

 ` `

Output:

```1 2 4 8 16 22 26 38 62 74
```

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