Re: [math-fun] Only eight

"... is there an n for which the decimal digit d does not appear in any power of two exactly n times?" I can example this now in another (normal) base. In base five, there are no powers of two where the digit 3 appears exactly 20848 times. The number of powers for nearby n is: 20844, 21; 20845, 9; 20846, 14; 20847, 10; 20849, 15; 20850, 12; 20851, 11; 20852, 10. On average there are 11.61 powers with (in my range) as many as 34. The next n for which the digit 3 does not appear exactly n times is greater than 250000. Other no-shows in base five: digit 0: n = 134212, 201042. digit 1: n = 160628, 166885, 180012. digit 2: n = 40634, 91291, 159058. digit 4: n = 75882, 232658.