144 - What Next?

[EratosthenesII]

Perfect squares end in 1,4,5,6,9 and zero. Nice symmetry.

Especially with the squares of

1 & 9 (5 +/- 4) ending in 1

2 & 8 (5 +/- 3) ending in 4

5 (5 +/- 0) ending in 5

4 & 6 (5 +/- 1) ending in 6

3 & 7 (5 +/- 2) ending in 9

 

 

WHAT ABOUT SQUARE ENDINGS?

100, 400, 900, 1600; of course, if a number ends with a zero, its square ends in 00

 

Is the only other repeated end for a square 44?

 

144 1444 3844 7744 12544 19044 26244 35344 44944 56644 68644

 

are all perfect squares

 

their square roots are (50n +/-12)² and n = 0,1,2 . . .

 

For further amusement, 213,444 = 462², and is the second member of a series (500n +/- 38)² = . . . 444

 

The comment is -

These two series should have names

 

[Fuzzwood]

Then give them ones!