If you follow the pattern, every palindrome of consecutive numbers has a square root made entirely of 1’s. Perfect logic, or just math playing games with our heads?
This is the result of convolution of a window of 1s (rectangular) with itself, which gives a triangular window. Convolution is the same as long multiplication that happens to not need any carries.
The pattern holds if the number of digits in the root are one less than the base. Obvious if you represent it visually. I love number theory. Am just learning it autodidactically x.com/fermatslibrary/status/…