At the August Bank Holiday Rapid-Play at the Hastings Chess Club I somehow did well enough to win a £5 book voucher. I spent it on "Professor Stewart's Incredible Numbers". On page 46 there is an account of numbers that cannot be expressed as a sum of three squares. A-M. Legendre found the formula (4^k)(8n + 1) for all such numbers. Here is a figured tour that I just constructed this afternoon showing all the Legendre Numbers less than 65 on the diagonals.