Blog Post #70 - Sum of successive squares - what do we observe?

Take a look at the series below - first 20 set of sum of successive squares

1 ^ 2 + 2 ^ 2 = 5
2 ^ 2 + 3 ^ 2 = 13
3 ^ 2 + 4 ^ 2 = 25
4 ^ 2 + 5 ^ 2 = 41
5 ^ 2 + 6 ^ 2 = 61
6 ^ 2 + 7 ^ 2 = 85
7 ^ 2 + 8 ^ 2 = 113
8 ^ 2 + 9 ^ 2 = 145
9 ^ 2 + 10 ^ 2 = 181
10 ^ 2 + 11 ^ 2 = 221
11 ^ 2 + 12 ^ 2 = 265
12 ^ 2 + 13 ^ 2 = 313
13 ^ 2 + 14 ^ 2 = 365
14 ^ 2 + 15 ^ 2 = 421
15 ^ 2 + 16 ^ 2 = 481
16 ^ 2 + 17 ^ 2 = 545
17 ^ 2 + 18 ^ 2 = 613
18 ^ 2 + 19 ^ 2 = 685
19 ^ 2 + 20 ^ 2 = 761
20 ^ 2 + 21 ^ 2 = 841

What all do we observe and are there specific inferences?

Blog Post #69 - Is this pattern a unique behaviour or just a coincidence?

Consider these numbers

131 - Prime number, Its anagrams 113 and 311 are prime as well
919 - Prime number, Its anagrams 199 and 991 are prime as well
373 - Prime number, Its anagrams 733 and 337 are prime as well

Is there a pattern or does it break somewhere? Does it also extend to 4 digit numbers?

Even if it breaks somewhere is there something that is common to all these numbers?

Blog Post #68 - What's unique about this series

What are the unique attributes about this series

576, 676, 5476, 5776, 15376, 15876

List all possible observations and is there any other series similar to this

Blog Post #67 - Find the 3 digit number

1. Let's call the number as XYZ
2. XYZ + a ^ 2 = Perfect square while XYZ - a^2 is a Prime number
3. XYZ + b ^ 2 = Perfect square while XYZ - b ^2 is again a Prime number
4. Suffix a digit W and XYZW is a perfect square again
5. XYZ itself is unique in some sense 

Blog Post #66 - What's the next series and why?

Looking at the series below, find the missing numbers

64, 81, 125, 144, 216, 289, ?, ?

Anything else unique about the result?

Blog Post # 65 - What is unique about these sequence of numbers?

I just happened to notice this pattern when I saw two cars with registration numbers 2809 and 1521 earlier today. Needless to say both number caught my attention since they were perfect squares and then tried to see if few more numbers exhibit that pattern

Here's the sequence I am looking at

1521, 2025, 2809, 4225, 4900...

It is obvious that they are perfect squares but there is something unique they exhibit apart from that in a sequence

What is the pattern they exhibit and also give me the next 2 or 3 four digit numbers in that sequence?

Blog #64 - Dedicated to Viswanathan Anand, the Chess Grandmaster!

Blog # 64 dedicated to the evergreen GOD of Chess - Viswanathan Anand!

New planet named after him with the number 4538 and the number does seems to be pretty special!

4538 - Square (53) + 1729 (Maths Genius Ramanujam Number!)
4538 - Square (67) + Square (7)
4538 - Square (64) + Square (21) + Square (1)

Anand has been the "King of 64 squares" in the Chess world and truly the number above does reflect that as well

And coincidentally this is also my 64th Blog!