# Look at me - a number sequence

This sequence goes on forever, but here is the first 7 of them. The X's are just there to hide the actual digits. Can you find all the correct digits of the 8th entry?

1024, 90X1X, 25023X, 490364, X1031X0, XX1041X4, X690XXXX, ________?

Hint:

No complicated calculations needed. In fact, it's based on a very simple rule. I'm sure this sequence would've been solved within minutes if I didn't replaced the digits with X's.

More specific hint:

Squares involved

• Does the use of 'X' represent the sameness of all digits? Jun 4 '20 at 17:03
• @JohnBrookfields No, it doesn't. Jun 4 '20 at 17:06

The pattern is

1024, 90X1X, 25023X, 490364, X1031X0, XX1041X4, X690XXXX
1024, 90216, 250236, 490364, 8103100, 12104144, 16904196

Hence, the next number is

22505256

• Why 05 in the middle vs. 04? Jun 4 '20 at 17:08
• Yes, that's also something that confused me. It seems like it increases every two numbers, but then 02 occurs thrice, so I'm not sure anymore. Jun 4 '20 at 17:10
• @sedrick well done, but the mid number is incorrect. The mid numbers represents something else Jun 4 '20 at 17:15

The fist few digits represent the odd number squares and the last few digits represent the even number square. ($$1^2$$ and $$2^2$$, $$3^2$$and $$4^2$$ and so on.) So, the next number will be $$22504256$$. The numbers given are: $$1024, 90216, 250236, 490364, 8103100, 12104144, 16904196$$ and finally $$22504256$$

• Good work, but the mid number is not correct. Take a look on the comment section above Jun 4 '20 at 17:26