Skip to main content

Problem 44 Project Euler Solution with python

Pentagon numbers

Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.
Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are pentagonal and D = |Pk − Pj| is minimised; what is the value of D?


I have wasted almost three days to solve this question, thinking in a very complicated way. I have read a lot of pdf's and websites online thinking that there should be a very complicated approach to solve this problem. Some of the papers which I have read are as follows:
Arithmetic of Pentagonal Numbers - Fibonacci quaterly
The pentagonal number theorem
Pentagonal Numbers - Wikipedia 
Pentagonal Numbers - Wolfram Math 
Pentagonal Numbers - Mathisfun 
Pentagonal Numbers - Fun way to learn math 
But none of them had any impact on my solution except the Wikipedia page which gave me information to check if the given number is pentagonal number or not.
The formula to check if the given number 'n' is pentagonal number or not is:
(1+(24n+1)1/2)/6 is an integer or not.

 A simple looping will yield the result.

Program

You can download the source code from Gist Github pep44.py

Output

Summary

I personally don't think that this problem deserves the Project Euler list. But anyhow they have added this problem on the website and I have written the solution. I am not fully satisfied with the solution. I have also thought of using two for loops with upper limit of 1 million for the first loop. That would have also worked.

 You can comment in the comment box below if you have any doubt or didn't understand anything. I will be glad to help you.

 Please do comment if you have found any typo or have a different program or better program or have any suggestion. I will be very happy to view each of them.

 You can also contact me.

 Thank you. Have a nice day😃.
Labels:

Popular posts from this blog

Problem 60 Project Euler Solution with python

Prime pair sets The primes 3, 7, 109, and 673, are quite remarkable. By taking any two primes and concatenating them in any order the result will always be prime. For example, taking 7 and 109, both 7109 and 1097 are prime. The sum of these four primes, 792, represents the lowest sum for a set of four primes with this property. Find the lowest sum for a set of five primes for which any two primes concatenate to produce another prime. This problem is j u st a brute force problem. If you have come here because you don't know the limit upto which you will h ave to gener ate the prime numbers t hen go ahe ad and t r y with 10,000 . When I first start ed solving the problem I chose 1 million(beca use most of the problem s on project E uler have this limit ), but it took very long for the computer to fin d the solution. After searching on the internet then I found many people choosing 10, 000 so I have changed my in put f rom 1 million to 10000 and the output was f ast. He...
Read more

Add/Embed SVG to Blogger website

In this post I will tell you my method(trick) of adding SVG images in a blogger website or blog. Before starting , the first thin g I am assu m ing is that you are aware of SVG if you are here. If not please see S calable V ec tor G raphics Recently when I tried to embed a SVG image for a post on pygal, I tried uploading the SVG file and blogger Image uploader came up with an error, because of which I had to find some other way.  SVG File upload Error in Blogger  I started sea rc hing Google " Embed SVG in Blogger " . I found blogorrhea , w h ich gave some i nformatio n on add ing SVG directly as a markup , which worked , but I faced another problem using this . Also th is guy has used lot of Javascript which was confusin g for me, being new to using SVG.   So I first t houg ht of learning on h ow to embed SVG in HTML and t his on e worked out. Actually we can embed SVG in HTML i n following ways: Using Object tag Using Iframe tag Using embed...
Read more

Making a quiz web app with python and flask

Edit : When you are creating a web app with h tml templates, then y ou will have to sa ve the html file in templates folder in the Current Wor ki ng Directory( CWD). If you save the file in the C W D directl y you will get a TemplateNotFound error. Thank you Udhay for pointing it out.   In this post we will create a quiz website using python . I will be using the flask framework . After reading this tutorial you will learn form submission , flask templates , python code in flask templates , shuffling the questions and options with the random module and few others.  Please note that this tutorial is not big as it seems to be. Some of the code has been rewritten to maintain consistency and also font size is somewhat big so that your eyes won't get stressed reading this tutorial. Also the content has not occupied the full width of the page. In this tutorial I am assuming that you are having a very basic understanding of the flask framework . Please refer the documenta...
Read more