# Smarandache-Wellin Sequence

Given a number ‘n’, generate the first ‘n’ terms of the Smarandache-Wellin Sequence.
The Smarandache-Wellin Sequence is a sequence formed by the Smarandache-Wellin numbers. Each Smarandache-Wellin number that make up the sequence is obtained by concatenating the consecutive prime numbers beginning from the first prime number i.e, 2. Thus, the first term of the sequence is 2, second term is 23, third term is 235, …. Similarly, the ‘n’th term is made up by concatenating the first ‘n’ prime numbers beginning from the first prime number i.e, 2.

Examples:

```Input : 5
Output : 2 23 235 2357 235711

Input : 10
Output : 2 23 235 2357 235711 23571113 2357111317 235711131719 23571113171923
2357111317192329
```

Approach:
1) Initially find the first ‘n’ prime numbers and store them in a list.
2) Next, concatenate each term of the list beginning from the first term and increasing the length of the concatenated term each time by one.
3) Keep printing the concatenated terms so formed, each time, to generate the sequence.

Below is the implementation in Python.

## Java

 `// Java program to print the  ` `// first 'n' terms of the ` `// Smarandache-Wellin Sequence ` ` `  `class` `GFG{ ` `// Function to collect ` `// first 'n' prime numbers ` `static` `void` `primes(``int` `n) ` `{ ` `    ``int` `i = ``2``; ` `    ``int` `j = ``0``; ` `     `  `    ``// List to store ` `    ``// first 'n' primes ` `    ``int``[] result=``new` `int``[n]; ` `    ``int` `z = ``0``; ` `    ``while``(j < n) ` `    ``{ ` `        ``boolean` `flag = ``true``; ` `        ``for``(``int` `item = ``2``;item <= (``int``)(i * ``1` `/ ``2``); item++) ` `            ``if``(i % item == ``0` `&& i != item) ` `            ``{ ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `        ``if` `(flag) ` `        ``{ ` `            ``result[z++] = i; ` `            ``j += ``1``; ` `        ``} ` `        ``i += ``1``; ` `    ``} ` ` `  `    ``for``(i = ``0``; i < result.length; i++) ` `    ``{ ` `        ``for``(j = ``0``; j <= i; j++) ` `            ``System.out.print(result[j]); ` `        ``System.out.print(``" "``); ` `    ``} ` `} ` ` `  `// Function to generate  ` `// Smarandache-Wellin Sequence ` `static` `void` `smar_wln(``int` `n) ` `{ ` `    ``// Storing the first 'n' ` `    ``// prime numbers in a list ` `    ``primes(n); ` `     `  `} ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `int` `n = ``5``; ` `System.out.println(``"First "``+n+``" terms of the Sequence are"``); ` `smar_wln(n); ` `} ` `} ` `// This code is contributed ` `// by mits  `

## Python3

 `# Python program to print the first 'n' terms ` `# of the Smarandache-Wellin Sequence ` ` `  `from` `__future__ ``import` `print_function ` ` `  `# Function to collect first 'n' prime numbers ` ` `  `def` `primes(n): ` `    ``i, j ``=` `2``, ``0` `    ``# List to store first 'n' primes ` `    ``result ``=` `[] ` `    ``while` `j < n: ` `        ``flag ``=` `True` `        ``for` `item ``in` `range``(``2``, ``int``(i``*``*``0.5``)``+``1``): ` `            ``if` `i ``%` `item ``=``=` `0` `and` `i !``=` `item: ` `                ``flag ``=` `False` `                ``break` `        ``if` `flag: ` `            ``result.append(i) ` `            ``j ``+``=` `1` `        ``i ``+``=` `1` `    ``return` `result ` ` `  `# Function to generate Smarandache-Wellin ` `# Sequence ` ` `  `def` `smar_wln(n): ` `    ``# Storing the first 'n' prime numbers in ` `    ``# a list ` `    ``arr ``=` `primes(n) ` `    ``for` `i ``in` `range``(``0``, ``len``(arr)): ` `        ``for` `j ``in` `range``(``0``, i ``+` `1``): ` `            ``print``(arr[j], end ``=``'') ` `        ``print``(end ``=``' '``) ` ` `  `# Driver Method ` ` `  `if` `__name__``=``=``'__main__'``: ` `    ``n ``=` `5` `    ``print``(``'First {} terms of the Sequence are\n'``.``format``(n)) ` `    ``smar_wln(n) `

## C#

 `// C# program to print the  ` `// first 'n' terms of the ` `// Smarandache-Wellin Sequence ` `class` `GFG ` `{ ` `// Function to collect ` `// first 'n' prime numbers ` `static` `void` `primes(``int` `n) ` `{ ` `    ``int` `i = 2; ` `    ``int` `j = 0; ` `     `  `    ``// List to store ` `    ``// first 'n' primes ` `    ``int``[] result = ``new` `int``[n]; ` `    ``int` `z = 0; ` `    ``while``(j < n) ` `    ``{ ` `        ``bool` `flag = ``true``; ` `        ``for``(``int` `item = 2;  ` `                ``item <= (``int``)(i * 1 / 2); item++) ` `            ``if``(i % item == 0 && i != item) ` `            ``{ ` `                ``flag = ``false``; ` `                ``break``; ` `            ``} ` `        ``if` `(flag) ` `        ``{ ` `            ``result[z++] = i; ` `            ``j += 1; ` `        ``} ` `        ``i += 1; ` `    ``} ` ` `  `    ``for``(i = 0; i < result.Length; i++) ` `    ``{ ` `        ``for``(j = 0; j <= i; j++) ` `            ``System.Console.Write(result[j]); ` `        ``System.Console.Write(``" "``); ` `    ``} ` `} ` ` `  `// Function to generate  ` `// Smarandache-Wellin Sequence ` `static` `void` `smar_wln(``int` `n) ` `{ ` `    ``// Storing the first 'n' ` `    ``// prime numbers in a list ` `    ``primes(n); ` `     `  `} ` ` `  `// Driver Code ` `static` `void` `Main() ` `{ ` `    ``int` `n = 5; ` `    ``System.Console.WriteLine(``"First "` `+ n +  ` `             ``" terms of the Sequence are"``); ` `    ``smar_wln(n); ` `} ` `} ` ` `  `// This code is contributed by mits  `

## PHP

 ` `

Output

```First 5 terms of the Sequence are

2 23 235 2357 235711
```

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Improved By : Mithun Kumar