Perfect Squares Last Digit Sequence

One day in middle school, I was playing with perfect squares 0, 1, 4, 9, 16, 25, 36, 49, 64, 81…

The last digits were: 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0
It is a palindrome!

Continuing: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 361…

The final digits went 0 1 4 9 6 5 6 9 4 1 0 1 4 9 6 5 6 9 4 1 0
0 (1496) 5 (6941) is a repeating bit so stringing them together, it looks like

0 (1496) 5 (6941) 0 (1496) 5 (6941) 0 (1496) 5 (6941) 0 (1496) 5 (6941) 0 (1496) 5 (6941) 0

This is a really pretty periodicity!

The workbook I played with this in is here :)
Originally published here :)

(see another beautiful periodicity in the Perfect Squares Digital Root Sequence)

0, 1, 4, 9, 6, 5, 6, 9, 4, 1