The StairCase-Sequence

A nano project on a novel number sequence.

UPDATE: Check out http://easypasswordgen.bitballoon.com/ to have a look on what we built. It is a JS based password generator that uses staircase numbers to generate easy to remember passwords.

A brief intro

Back in June 2016, I discovered a novel number sequence. Just like the sequence of numbers: 0,1,1,2,3,5,8,13... are named as fibonacci sequence, I named my number sequence as "The staircase sequence".
Eventually I wrote down my work and the staircase sequence got accepted in the OEIS or the Online Encyclopedia of Integer Sequences.
You can visit http://oeisf.org to know more about OEIS.
You can visit http://oeis.org to use the OEIS database.

What is a staircase number ?

A number with atleast three digits and with the property that the sum of the squares of the first and last digits equals the number obtained when the first and last digits are deleted.
For example, let us take an example of the number: 81137
Take the first digit 8 and make its square. It is 64.
Again take the last digit 7 and make its square. It is 49.
Now add both of them: 64 + 49 = 113.
Thus 113 happens to be the middle digits of 81137.And hence 81137 is a staircase number.

What is the staircase sequence?

The staircase sequence is the sequence of all staircase number sorted in ascending order starting from 110 and continuing till infinity.
Below are some of the initial terms of the staircase sequence:
110, 121, 152, 240, 251, 282, 390, 1010, 1021, 1052, 1103, 1174, 1265, 1376, 1507, 1658, 1829, 2040, 2051, 2082, 2133, 2204, 2295, 2406, 2537, 2688, 2859, 3090, 3101, 3132, 3183, 3254, 3345, 3456, 3587, 3738, 3909, 4160, 4171, 4202, 4253, 4324, 4415, 4526, 4657, 4808, 4979, 5250, 5261, 5292, 5343, 5414, 5505, 5616 ............. infinity.
To get the the first 10,000+ terms you can visit: http://oeis.org/A274945/b274945.txt

For whom is the project?

The project targets a wide audience. People from academia to developers, from open source newbies to experienced developers.
The target audience is described as follows:

• For computer programmers: Programmers can write improved algorithms for printng the staircase sequence. They can write it in C,C++,Java,Javascript or any of their competent language as multi language support is very necessary.They can also write up algorithms and programs to find the nth term of the sequence.
• For developers: The role of developers is quite interesting. Developers can develop applications that use the staircase sequence. Like an easy to remember password generator. They can develop applications and deploy them for the normal people to use.
• For professional and amateur mathematicians: People with expertise and passion in the field of mathematics can look into the theoretical aspects of the project. They can work in finding non-trivial properties of the sequence and work on formulaes for finding out the nth term of the sequence. They can also try bringing different versions of the staircase sequence. Like there exists a version of the staircase sequence where the sequence starts at 110 but ends at 91629. You can visit: http://oeis.org/A274944 to know more.

What is the goal of the project?

The project covers a wide and diverse set of goals. Starting from programming the sequence in multiple languages and with a better algorithmic approach to developing web applications like easy to remember password generator based on the number sequence. We are also looking for some interesting non-trival properties that may be hidden within the sequence.
The primary goals include (but not limited to):

• Spreading the awarness about the Staircase Sequence
• Developing better algorithms to print the Staircase Sequence.
• Finding out some non-trivial and interesting application and/or theory on the sequence.
• Developing the algorithms that print staircase numbers in multiple languages.
• Developing applications (web or android or others) that uses the staircase sequence.
  Like a website that could generate easy to remember passwords using staircase numbers.
• Developing a program that could generate the staircase graph from the staircase sequence.
  To see an example visit: http://oeis.org/A274945/graph .
• Eventually, contributing the most significant works to the OEIS in terms of codes or theory or both.

So how shall I get involved?

Well, so head on to the issues tab : https://github.com/Bisso1998/StairCase-Sequence/issues
You will find several open issues. Try working on any issue you like.
If you are the first timer, then you must watch the video: https://www.youtube.com/watch?v=_NrSWLQsDL4
It discusses in a very well manner on how to generate pull requests. In short, fork the staircase repository. Clone it in your computer. Commit the changes that you want to make. Then finally make a pull request. If your work is
We are open to pull requests.

What is in there for me apart from contributing to the repository?

So apart from contributing to the repository, the most significant works will be forwarded to the OEIS foundation for getting updated into their OEIS database (after due scrutiny by the OEIS editors board). All the contibutors will be given due credit for their work if their work is updated in the OEIS website.

Hoping to get a lot many pull requests.
Happy coding