| k | a | no need to check | ratio (%) of omittable case |
|---|---|---|---|
| 2 | 4 | 3 | 75.00 |
| 3 | 8 | 6 | 75.00 |
| 4 | 16 | 13 | 81.25 |
| 5 | 32 | 28 | 87.50 |
| 6 | 64 | 56 | 87.50 |
| 7 | 128 | 115 | 89.84 |
| 8 | 256 | 237 | 92.58 |
| 9 | 512 | 474 | 92.58 |
| 10 | 1024 | 960 | 93.75 |
| 11 | 2048 | 1920 | 93.75 |
| 12 | 4096 | 3870 | 94.48 |
| 13 | 8192 | 7825 | 95.52 |
| 14 | 16384 | 15650 | 95.52 |
| 15 | 32768 | 31473 | 96.05 |
| 16 | 65536 | 63422 | 96.77 |
| 17 | 131072 | 126844 | 96.77 |
| 18 | 262144 | 254649 | 97.14 |
| 19 | 524288 | 509298 | 97.14 |
| 20 | 1048576 | 1021248 | 97.39 |
For example, the case 220+b (b=1, ... , 220-1),
1021248 cases are omittable, only 27328 cases are necessary out of 220=1048576.
| n | max(n) |
|---|---|
| 27 | 9232 |
| 447 | 39364 |
| 639 | 41524 |
| 703 | 250504 |
| 1819 | 1276936 |
| 4255 | 6810136 |
| 4591 | 8153620 |
| 9663 | 27114424 |
| 20895 | 50143264 |
| 26623 | 106358020 |
| 31911 | 121012864 |
| 60975 | 593279152 |
| 77671 | 1570824736 |
| 113383 | 2482111348 |
| 138367 | 2798323360 |
| 159487 | 17202377752 |
| 270271 | 24648077896 |
| 665215 | 52483285312 |
| 704511 | 56991483520 |
| 1042431 | 90239155648 |
| 1212415 | 139646736808 |
| 1441407 | 151629574372 |
| 1875711 | 155904349696 |
| 1988859 | 156914378224 |
| 2643183 | 190459818484 |
| 2684647 | 352617812944 |
| 3041127 | 622717901620 |
| 3873535 | 858555169576 |
| 4637979 | 1318802294932 |
| 5656191 | 2412493616608 |
| 6416623 | 4799996945368 |
| 6631675 | 60342610919632 |
| 19638399 | 306296925203752 |
| 38595583 | 474637698851092 |
| 80049391 | 2185143829170100 |
| 120080895 | 3277901576118580 |
| 210964383 | 6404797161121264 |
| 319804831 | 1414236446719942480 |
| 1410123943 | 7125885122794452160 |
| 8528817511 | 18144594937356598024 |
So, what kind of relations between n and max(n) ?
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