Am I doing something wrong? I get 94.9% for 243/256 243 is pretty good. You have to go up to 3^17 = 129140163 < 2^27 = 134217728 to beat it: 1

Am I doing something wrong? I get 94.9% for 243/256 243 is pretty good. You have to go up to 3^17 = 129140163 < 2^27 = 134217728 to beat it: 1 3 4 2 1 75.0%* 2 9 16 4 7 56.2% 3 27 32 5 5 84.4%* 4 81 128 7 47 63.3% 5 243 256 8 13 94.9%* 6 729 1024 10 295 71.2% 7 2187 4096 12 1909 53.4% 8 6561 8192 13 1631 80.1% 9 19683 32768 15 13085 60.1% 10 59049 65536 16 6487 90.1% 11 177147 262144 18 84997 67.6% 12 531441 1048576 20 517135 50.7% 13 1594323 2097152 21 502829 76.0% 14 4782969 8388608 23 3605639 57.0% 15 14348907 16777216 24 2428309 85.5% 16 43046721 67108864 26 24062143 64.1% 17 129140163 134217728 27 5077565 96.2%* 18 387420489 536870912 29 149450423 72.2% 19 1162261467 2147483648 31 985222181 54.1% 20 3486784401 4294967296 32 808182895 81.2% 21 10460353203 17179869184 34 6719515981 60.9% 22 31381059609 34359738368 35 2978678759 91.3% 23 94143178827 137438953472 37 43295774645 68.5% 24 282429536481 549755813888 39 267326277407 51.4% 25 847288609443 1099511627776 40 252223018333 77.1% 26 2541865828329 4398046511104 42 1856180682775 57.8% 27 7625597484987 8796093022208 43 1170495537221 86.7% 28 22876792454961 35184372088832 45 12307579633871 65.0% 29 68630377364883 70368744177664 46 1738366812781 97.5%* 30 205891132094649 281474976710656 48 75583844616007 73.1% 31 617673396283947 1125899906842624 50 508226510558677 54.9% 32 1853020188851841 2251799813685248 51 398779624833407 82.3% 33 5559060566555523 9007199254740992 53 3448138688185469 61.7% 34 16677181699666569 18014398509481984 54 1337216809815415 92.6% 35 50031545098999707 72057594037927936 56 22026048938928229 69.4% 36 150094635296999121 288230376151711744 58 138135740854712623 52.1% 37 450283905890997363 576460752303423488 59 126176846412426125 78.1% 38 1350851717672992089 2305843009213693952 61 954991291540701863 58.6% 39 4052555153018976267 4611686018427387904 62 559130865408411637 87.9% Generated with this: max_use = 0 for i in range(1, 40): trinary = 3**i power = math.ceil(math.log2(trinary)) binary = 2**int(power) diff = binary - trinary use = (trinary / binary) max_star = '' if use > max_use: max_use = use max_star = '*' print(f' {i:2} {trinary:19} {binary:19} {power:2} {diff:18} {use:.1%}{max_star}')