{"id":12639,"date":"2022-08-23T15:00:58","date_gmt":"2022-08-23T09:30:58","guid":{"rendered":"https:\/\/btechgeeks.com\/?p=12639"},"modified":"2022-08-23T15:15:11","modified_gmt":"2022-08-23T09:45:11","slug":"python-program-to-generate-first-n-numbers-of-pell-series","status":"publish","type":"post","link":"https:\/\/btechgeeks.com\/python-program-to-generate-first-n-numbers-of-pell-series\/","title":{"rendered":"Pell series &#8211; Python Program to Generate first N numbers of Pell Series"},"content":{"rendered":"<p><strong>Pell series: <\/strong>Given the number N, the task is to print the first n numbers of the pell series in Python.<\/p>\n<p><strong>Pell Series:<\/strong><\/p>\n<blockquote><p>The Pell Series is a series in which the next number equals the sum of twice the previous number and the number preceding the previous number.<\/p>\n<p>It begins with 1 and 2.<\/p>\n<p>Pell Numbers: 1,2,5,12,29,70,169,&#8230;<\/p>\n<p>Consider the following number sequence and try to match it to the definition of the Pell Series:<\/p>\n<p>1 + 2 x 2 = 5<\/p>\n<p>2 + 5* 2 = 12<\/p>\n<p>5 + 12 x 2 = 29<\/p>\n<p>12 + 29*2 = 70<\/p>\n<p>29 + 70*2 = 169<\/p>\n<p>and so on\u2026<\/p><\/blockquote>\n<p>Now that you have a clear idea of what the Pell Series are, let\u2019s move on to how we shall write the Python code to generate the same.<\/p>\n<ul>\n<li><a href=\"https:\/\/btechgeeks.com\/java-program-to-print-pell-number-series-0-1-2-5-12-29-70-n\/\">Java Program to Print Pell Number Series 0 1 2 5 12 29 70 \u2026N<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-find-sum-of-series-11-122-233-3-nn-n\/\">Python Program to Find Sum of Series 1^1\/1+2^2\/2+3^3\/3&#8230;+n^n\/n<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-find-the-sum-of-series-1-x-x2-2-xn-n\/\">Python Program to Find the Sum of Series 1+X+X^2\/2&#8230;+X^N\/N<\/a><\/li>\n<\/ul>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<pre>Given number = 12<\/pre>\n<p><strong>Input:<\/strong><\/p>\n<pre>The first 12 numbers of the pell series are :\r\n1 2 5 12 29 70 169 408 985 2378 5741 13860<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given number = 21<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The first 21 numbers of the pell series are :\r\n1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109\r\n 15994428 38613965<\/pre>\n<h2>Program to Generate first N numbers of Pell Series in Python<\/h2>\n<p>Below are the ways to generate the first N number of the pell series in Python.<\/p>\n<ul>\n<li><a href=\"#Using_For_loop(Static_Input)\">Using For loop(Static Input)<\/a><\/li>\n<li><a href=\"#Using_For_loop(User_Input)\">Using For loop(User Input)<\/a><\/li>\n<\/ul>\n<p>If you are new to Java and want to learn the java coding skills too fast. Try practicing the core java programs with the help of the <a href=\"https:\/\/btechgeeks.com\/python-programming-examples-with-output\/\">Java basic programs list<\/a> available.<\/p>\n<h3 id=\"Using_For_loop(Static_Input)\">Method #1: Using For Loop (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the number N as static input and store it in a variable.<\/li>\n<li>Take a variable temp1 and initialize it to 1.<\/li>\n<li>Take another variable temp2 and initialize it to 2.<\/li>\n<li>Take the third variable temp3 and initialize it to 0.<\/li>\n<li>Now, print the first two numbers in the series, and we&#8217;ll print the other generated numbers in the order they were generated.<\/li>\n<li>Loop till number -2 using For loop.<\/li>\n<li>Add the value of temp1 and twice the temp2 value and initialize the temp3 with this value.<\/li>\n<li>Swap the previous number for the previous number&#8217;s predecessor (temp1 =temp2).<\/li>\n<li>Swap the generated and previously generated numbers (temp2 = temp3).<\/li>\n<li>Print the value of temp3.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Give the number N as static input and store it in a variable.\r\nnumb = 21\r\n# Take a variable temp1 and initialize it to 1.\r\ntemp1 = 1\r\n# Take another variable temp2 and initialize it to 2.\r\ntemp2 = 2\r\n# Take the third variable temp3 and initialize it to 0.\r\ntemp3 = 0\r\n# Now, print the first two numbers in the series,\r\n# and we'll print the other generated numbers in the order they were generated.\r\nprint('The first', numb, 'numbers of the pell series are :')\r\nprint(temp1, temp2, end=' ')\r\n# Loop till number -2 using For loop.\r\nfor i in range(numb-2):\r\n    # Add the value of temp1 and twice the temp2 value\r\n    # and initialize the temp3 with this value.\r\n    temp3 = temp1+2*temp2\r\n    # Swap the previous number for the previous number's predecessor (temp1 =temp2).\r\n    temp1 = temp2\r\n    # Swap the generated and previously generated numbers (temp2 = temp3)\r\n    temp2 = temp3\r\n    # Print the value of temp3.\r\n    print(temp3, end=' ')\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The first 21 numbers of the pell series are :\r\n1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109\r\n 15994428 38613965<\/pre>\n<h3 id=\"Using_For_loop(User_Input)\">Method #2: Using For Loop (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give the number N as user input using int(input()) and store it in a variable.<\/li>\n<li>Take a variable temp1 and initialize it to 1.<\/li>\n<li>Take another variable temp2 and initialize it to 2.<\/li>\n<li>Take the third variable temp3 and initialize it to 0.<\/li>\n<li>Now, print the first two numbers in the series, and we&#8217;ll print the other generated numbers in the order they were generated.<\/li>\n<li>Loop till number -2 using For loop.<\/li>\n<li>Add the value of temp1 and twice the temp2 value and initialize the temp3 with this value.<\/li>\n<li>Swap the previous number for the previous number&#8217;s predecessor (temp1 =temp2).<\/li>\n<li>Swap the generated and previously generated numbers (temp2 = temp3).<\/li>\n<li>Print the value of temp3.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Give the number N as user input using int(input()) and store it in a variable.\r\nnumb = int(input('Enter some random number = '))\r\n# Take a variable temp1 and initialize it to 1.\r\ntemp1 = 1\r\n# Take another variable temp2 and initialize it to 2.\r\ntemp2 = 2\r\n# Take the third variable temp3 and initialize it to 0.\r\ntemp3 = 0\r\n# Now, print the first two numbers in the series,\r\n# and we'll print the other generated numbers in the order they were generated.\r\nprint('The first', numb, 'numbers of the pell series are :')\r\nprint(temp1, temp2, end=' ')\r\n# Loop till number -2 using For loop.\r\nfor i in range(numb-2):\r\n    # Add the value of temp1 and twice the temp2 value\r\n    # and initialize the temp3 with this value.\r\n    temp3 = temp1+2*temp2\r\n    # Swap the previous number for the previous number's predecessor (temp1 =temp2).\r\n    temp1 = temp2\r\n    # Swap the generated and previously generated numbers (temp2 = temp3)\r\n    temp2 = temp3\r\n    # Print the value of temp3.\r\n    print(temp3, end=' ')\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 12\r\nThe first 12 numbers of the pell series are :\r\n1 2 5 12 29 70 169 408 985 2378 5741 13860<\/pre>\n<p><strong>Related Programs<\/strong>:<\/p>\n<ul>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-generate-a-dictionary-that-contains-numbers-between-1-and-n-in-the-form-x-xx\/\">python program to generate a dictionary that contains numbers between 1 and n in the form x xx<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-find-the-sum-of-the-series-1-1-2-1-3-1-n\/\">python program to find the sum of the series 1 1 2 1 3 1 n<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-find-the-sum-of-the-series-1-x2-2-x3-3-xn-n\/\">python program to find the sum of the series 1 x2 2 x3 3 xn n<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/cpp-program-to-calculate-sum-of-first-n-natural-numbers\/\">cpp program to calculate sum of first n natural numbers<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/c-program-to-find-the-sum-of-first-n-natural-numbers\/\">c program to find the sum of first n natural numbers<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-print-first-k-digits-of-1-n-where-n-is-a-positive-integer\/\">python program to print first k digits of 1 n where n is a positive integer<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/python-program-to-find-the-sum-of-natural-numbers\/\">python program to find the sum of natural numbers<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Pell series: Given the number N, the task is to print the first n numbers of the pell series in Python. Pell Series: The Pell Series is a series in which the next number equals the sum of twice the previous number and the number preceding the previous number. It begins with 1 and 2. &#8230; <a title=\"Pell series &#8211; Python Program to Generate first N numbers of Pell Series\" class=\"read-more\" href=\"https:\/\/btechgeeks.com\/python-program-to-generate-first-n-numbers-of-pell-series\/\" aria-label=\"More on Pell series &#8211; Python Program to Generate first N numbers of Pell Series\">Read more<\/a><\/p>\n","protected":false},"author":7,"featured_media":12643,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pell series - Python Program to Generate first N numbers of Pell Series - BTech Geeks<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/btechgeeks.com\/python-program-to-generate-first-n-numbers-of-pell-series\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pell series - Python Program to Generate first N numbers of Pell Series - BTech Geeks\" \/>\n<meta property=\"og:description\" content=\"Pell series: Given the number N, the task is to print the first n numbers of the pell series in Python. 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Pell Series: The Pell Series is a series in which the next number equals the sum of twice the previous number and the number preceding the previous number. It begins with 1 and 2. ... 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