I had an idea -- 1. Get the sum of 3 squares sols for a number 8n+3, http://oeis.org/A017101 . 2. Get all +/- permutations, divide by 2, add 255/2. 3. Draw a sphere centered at (255/2,255/2,255/2) going though those points, and color all points within the RGB cube with their appropriate RGB value. I was surprised that 122707 led to a "dark" sphere. All of the sum of three squares sols, (1, 165,309), (1, 195, 291), ..., (35, 81, 261), ...(125, 171, 279), (147, 163, 273) had a value greater than 255, with 261 as the minimal maximum. So I looked for the first numbers that have a minimal maximum of 3, 5, 7, 9, and so on. 1099 has sum of 3 square sols (3, 27, 55), (15, 17, 57), (15, 27, 53), min max of 53. 11, 35, 67, 91, 195, 259, 235, 379, 555, 547, 763, 795, 1099, 1131, \ 1667, 1387, 1963, 2251, 2563, 2667, 2515, 3259, 3459, 3355, 4187, \ 3763, 5131, 4939, 5691, 6403, 6907, 7395, 7315, 7627, 7291, 9867, \ 9403, 10587, 10651, 8947, 11067, 11715, 11467, 14547, 14779, 13435, \ 15915, 15691, 15787, 19643, 14947, 18883, 21835, 19947, 20155, 23403, \ 25635, 24355, 27267, 28771, 24907, 24787, 28315, 26251, 34203, 30739, \ 32971, 34707, 33163, 35779, 37947, 40627, 37195, 42915, 43051, 43867, \ 43563, 42883, 46627, 49123, 51947, 39715, 54547, 53475, 51811, 57163, \ 58755, 56947, 58195, 64603, 57643, 60019, 71547, 70411, 69115, 75075, \ 69355, 75835, 77883, 71947, 81363, 72499, 76987, 82219, 89539, 88147, \ 90867, 90955, 93163, 98987, 93307, 99547, 93003, 105163, 103051, \ 107043, 107787, 111643, 112291, 116851, 112315, 120523, 121323, \ 116515, 121627, 124723, 122155, 127659, 133627, 122707 Turns out that 122707 is unusually low, following a number of higher values. 3763 and 8947 are two more like that. --Ed Pegg Jr