| A - Squares, Lists and Digital Sums |
Wherever there is a number, there is beauty.
Proclo
The list
81, 100, 121, 144, 169, 196, 225
consists of seven consecutive squares (from the square of 9 to 15). It has a curious feature: the sum of the decimal digits of each of these numbers is itself a square. For example, 1 + 6 + 9 = 16 = 42.
Find the next sequence of seven consecutive squares with the same property.
There is no input.
The output consists of seven lines. The first line contains two numbers,which are the first of the seven numbers we are looking for and its square. The second line contains two numbers,which are the second of the seven numbers we are looking for and its square. And so on.
For example, if we had asked you for the first sequence of seven numbers that meet the property, the output would have been as follows:
9 81 10 100 11 121 12 144 13 169 14 196 15 225