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发表于 2009-3-6 08:32:40
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显示全部楼层
我编了些程序，
得到 2^p*3^q*7^s 系列的整数，步数不小于 3 的有 587 组。
得到 3^q*5^s*7^r 系列的整数，步数不小于 3 的仅有 12 组：
| No. | steps | r(2,3,5,7) | value | | 1 | 4 | ( 0, 2, 2, 1 ) | 1575 | | 2 | 4 | ( 0, 1, 5, 2 ) | 59535 | | 3 | 4 | ( 0, 2, 2, 3 ) | 77175 | | 4 | 3 | ( 0, 2, 1, 0 ) | 75 | | 5 | 3 | ( 0, 2, 0, 1 ) | 175 | | 6 | 3 | ( 0, 1, 0, 3 ) | 1715 | | 7 | 3 | ( 0, 3, 3, 0 ) | 3375 | | 8 | 3 | ( 0, 5, 1, 0 ) | 9375 | | 9 | 3 | ( 0, 4, 2, 1 ) | 39375 | | 10 | 3 | ( 0, 3, 7, 2 ) | 13395375 | | 11 | 3 | ( 0, 8, 6, 1 ) | 1993359375 | | 12 | 3 | ( 0, 1, 18, 1 ) | 13559717115 |
以下是整理并排序后的数据（第一优先级是 steps 降序，第二优先级是 value 升序）：
| No. | steps | r(2,3,5,7) | value | | 1 | 10 | ( 19, 4, 0, 6 ) | 4996238671872 | | 2 | 10 | ( 4, 20, 0, 5 ) | 937638166841712 | | 3 | 9 | ( 12, 7, 0, 2 ) | 438939648 | | 4 | 9 | ( 33, 3, 0, 0 ) | 231928233984 | | 5 | 8 | ( 11, 7, 0, 0 ) | 4478976 | | 6 | 8 | ( 6, 6, 0, 5 ) | 784147392 | | 7 | 8 | ( 21, 3, 0, 3 ) | 19421724672 | | 8 | 8 | ( 1, 2, 0, 12 ) | 249143169618 | | 9 | 8 | ( 9, 5, 0, 8 ) | 717233481216 | | 10 | 7 | ( 8, 3, 0, 2 ) | 338688 | | 11 | 7 | ( 1, 10, 0, 1 ) | 826686 | | 12 | 7 | ( 10, 7, 0, 0 ) | 2239488 | | 13 | 7 | ( 1, 13, 0, 0 ) | 3188646 | | 14 | 7 | ( 4, 10, 0, 1 ) | 6613488 | | 15 | 7 | ( 9, 4, 0, 3 ) | 14224896 | | 16 | 7 | ( 6, 27, 0, 1 ) | 3416267673274176 | | 17 | 7 | ( 24, 18, 0, 0 ) | 6499837226778624 | | 18 | 6 | ( 10, 3, 0, 0 ) | 27648 | | 19 | 6 | ( 2, 5, 0, 2 ) | 47628 | | 20 | 6 | ( 0, 3, 0, 4 ) | 64827 | | 21 | 6 | ( 6, 3, 0, 2 ) | 84672 | | 22 | 6 | ( 27, 0, 0, 0 ) | 134217728 | | 23 | 6 | ( 5, 5, 0, 6 ) | 914838624 | | 24 | 6 | ( 10, 6, 0, 4 ) | 1792336896 | | 25 | 6 | ( 23, 2, 0, 2 ) | 3699376128 | | 26 | 6 | ( 1, 20, 0, 1 ) | 48814981614 | | 27 | 6 | ( 5, 6, 0, 8 ) | 134481277728 | | 28 | 6 | ( 16, 8, 0, 3 ) | 147483721728 | | 29 | 6 | ( 24, 6, 0, 6 ) | 1438916737499136 | | 30 | 5 | ( 7, 1, 0, 1 ) | 2688 | | 31 | 5 | ( 7, 1, 0, 2 ) | 18816 | | 32 | 5 | ( 2, 8, 0, 0 ) | 26244 | | 33 | 5 | ( 5, 2, 0, 3 ) | 98784 | | 34 | 5 | ( 3, 4, 0, 3 ) | 222264 | | 35 | 5 | ( 18, 0, 0, 0 ) | 262144 | | 36 | 5 | ( 12, 4, 0, 0 ) | 331776 | | 37 | 5 | ( 2, 5, 0, 3 ) | 333396 | | 38 | 5 | ( 3, 5, 0, 3 ) | 666792 | | 39 | 5 | ( 15, 1, 0, 1 ) | 688128 | | 40 | 5 | ( 16, 3, 0, 0 ) | 1769472 | | 41 | 5 | ( 6, 8, 0, 1 ) | 2939328 | | 42 | 5 | ( 9, 1, 0, 4 ) | 3687936 | | 43 | 5 | ( 12, 1, 0, 3 ) | 4214784 | | 44 | 5 | ( 11, 0, 0, 4 ) | 4917248 | | 45 | 5 | ( 5, 10, 0, 1 ) | 13226976 | | 46 | 5 | ( 7, 2, 0, 5 ) | 19361664 | | 47 | 5 | ( 2, 4, 0, 6 ) | 38118276 | | 48 | 5 | ( 15, 7, 0, 0 ) | 71663616 | | 49 | 5 | ( 16, 5, 0, 1 ) | 111476736 | | 50 | 5 | ( 1, 4, 0, 7 ) | 133413966 | | 51 | 5 | ( 2, 0, 0, 9 ) | 161414428 | | 52 | 5 | ( 21, 4, 0, 0 ) | 169869312 | | 53 | 5 | ( 5, 0, 0, 8 ) | 184473632 | | 54 | 5 | ( 3, 14, 0, 1 ) | 267846264 | | 55 | 5 | ( 6, 0, 0, 8 ) | 368947264 | | 56 | 5 | ( 7, 12, 0, 1 ) | 476171136 | | 57 | 5 | ( 20, 5, 0, 1 ) | 1783627776 | | 58 | 5 | ( 9, 2, 0, 7 ) | 3794886144 | | 59 | 5 | ( 9, 11, 0, 2 ) | 4444263936 | | 60 | 5 | ( 19, 2, 0, 4 ) | 11329339392 | | 61 | 5 | ( 12, 0, 0, 8 ) | 23612624896 | | 62 | 5 | ( 22, 6, 0, 2 ) | 149824733184 | | 63 | 5 | ( 9, 13, 0, 3 ) | 279988627968 | | 64 | 5 | ( 11, 2, 0, 9 ) | 743797684224 | | 65 | 5 | ( 14, 10, 0, 4 ) | 2322868617216 | | 66 | 5 | ( 5, 11, 0, 7 ) | 4668421498272 | | 67 | 5 | ( 14, 1, 0, 10 ) | 13884223438848 | | 68 | 5 | ( 6, 23, 0, 1 ) | 42176144114496 | | 69 | 5 | ( 39, 3, 0, 2 ) | 727326941773824 | | 70 | 5 | ( 35, 2, 0, 6 ) | 36381499733311488 | | 71 | 4 | ( 1, 3, 0, 1 ) | 378 | | 72 | 4 | ( 7, 1, 0, 0 ) | 384 | | 73 | 4 | ( 1, 0, 0, 3 ) | 686 | | 74 | 4 | ( 8, 1, 0, 0 ) | 768 | | 75 | 4 | ( 0, 2, 2, 1 ) | 1575 | | 76 | 4 | ( 2, 2, 0, 2 ) | 1764 | | 77 | 4 | ( 1, 3, 0, 2 ) | 2646 | | 78 | 4 | ( 1, 7, 0, 0 ) | 4374 | | 79 | 4 | ( 11, 1, 0, 0 ) | 6144 | | 80 | 4 | ( 1, 2, 0, 3 ) | 6174 | | 81 | 4 | ( 7, 0, 0, 2 ) | 6272 | | 82 | 4 | ( 10, 0, 0, 1 ) | 7168 | | 83 | 4 | ( 3, 1, 0, 3 ) | 8232 | | 84 | 4 | ( 2, 7, 0, 0 ) | 8748 | | 85 | 4 | ( 8, 2, 0, 1 ) | 16128 | | 86 | 4 | ( 4, 3, 0, 2 ) | 21168 | | 87 | 4 | ( 5, 6, 0, 0 ) | 23328 | | 88 | 4 | ( 4, 5, 0, 1 ) | 27216 | | 89 | 4 | ( 12, 0, 0, 1 ) | 28672 | | 90 | 4 | ( 5, 1, 0, 3 ) | 32928 | | 91 | 4 | ( 4, 7, 0, 0 ) | 34992 | | 92 | 4 | ( 4, 2, 0, 3 ) | 49392 | | 93 | 4 | ( 0, 1, 5, 2 ) | 59535 | | 94 | 4 | ( 2, 0, 0, 5 ) | 67228 | | 95 | 4 | ( 0, 2, 2, 3 ) | 77175 | | 96 | 4 | ( 9, 3, 0, 1 ) | 96768 | | 97 | 4 | ( 8, 2, 0, 2 ) | 112896 | | 98 | 4 | ( 6, 7, 0, 0 ) | 139968 | | 99 | 4 | ( 4, 3, 0, 3 ) | 148176 | | 100 | 4 | ( 5, 6, 0, 1 ) | 163296 | | 101 | 4 | ( 1, 7, 0, 2 ) | 214326 | | 102 | 4 | ( 2, 10, 0, 0 ) | 236196 | | 103 | 4 | ( 17, 1, 0, 0 ) | 393216 | | 104 | 4 | ( 1, 8, 0, 2 ) | 642978 | | 105 | 4 | ( 5, 2, 0, 4 ) | 691488 | | 106 | 4 | ( 12, 3, 0, 1 ) | 774144 | | 107 | 4 | ( 2, 4, 0, 4 ) | 777924 | | 108 | 4 | ( 3, 0, 0, 6 ) | 941192 | | 109 | 4 | ( 6, 7, 0, 1 ) | 979776 | | 110 | 4 | ( 1, 5, 0, 4 ) | 1166886 | | 111 | 4 | ( 0, 4, 0, 5 ) | 1361367 | | 112 | 4 | ( 6, 2, 0, 4 ) | 1382976 | | 113 | 4 | ( 2, 1, 0, 6 ) | 1411788 | | 114 | 4 | ( 11, 6, 0, 0 ) | 1492992 | | 115 | 4 | ( 10, 5, 0, 1 ) | 1741824 | | 116 | 4 | ( 6, 4, 0, 3 ) | 1778112 | | 117 | 4 | ( 8, 1, 0, 4 ) | 1843968 | | 118 | 4 | ( 4, 0, 0, 6 ) | 1882384 | | 119 | 4 | ( 1, 2, 0, 6 ) | 2117682 | | 120 | 4 | ( 5, 5, 0, 3 ) | 2667168 | | 121 | 4 | ( 4, 4, 0, 4 ) | 3111696 | | 122 | 4 | ( 16, 0, 0, 2 ) | 3211264 | | 123 | 4 | ( 5, 0, 0, 6 ) | 3764768 | | 124 | 4 | ( 6, 10, 0, 0 ) | 3779136 | | 125 | 4 | ( 6, 3, 0, 4 ) | 4148928 | | 126 | 4 | ( 13, 4, 0, 1 ) | 4644864 | | 127 | 4 | ( 0, 14, 0, 0 ) | 4782969 | | 128 | 4 | ( 5, 4, 0, 4 ) | 6223392 | | 129 | 4 | ( 8, 4, 0, 3 ) | 7112448 | | 130 | 4 | ( 20, 2, 0, 0 ) | 9437184 | | 131 | 4 | ( 10, 3, 0, 3 ) | 9483264 | | 132 | 4 | ( 16, 1, 0, 2 ) | 9633792 | | 133 | 4 | ( 14, 6, 0, 0 ) | 11943936 | | 134 | 4 | ( 7, 7, 0, 2 ) | 13716864 | | 135 | 4 | ( 1, 2, 0, 7 ) | 14823774 | | 136 | 4 | ( 24, 0, 0, 0 ) | 16777216 | | 137 | 4 | ( 16, 0, 0, 3 ) | 22478848 | | 138 | 4 | ( 14, 0, 0, 4 ) | 39337984 | | 139 | 4 | ( 4, 10, 0, 2 ) | 46294416 | | 140 | 4 | ( 3, 11, 0, 2 ) | 69441624 | | 141 | 4 | ( 17, 4, 0, 1 ) | 74317824 | | 142 | 4 | ( 12, 4, 0, 3 ) | 113799168 | | 143 | 4 | ( 8, 3, 0, 5 ) | 116169984 | | 144 | 4 | ( 4, 11, 0, 2 ) | 138883248 | | 145 | 4 | ( 0, 12, 0, 3 ) | 182284263 | | 146 | 4 | ( 23, 3, 0, 0 ) | 226492416 | | 147 | 4 | ( 8, 3, 0, 6 ) | 813189888 | | 148 | 4 | ( 19, 5, 0, 1 ) | 891813888 | | 149 | 4 | ( 1, 4, 0, 8 ) | 933897762 | | 150 | 4 | ( 0, 19, 0, 0 ) | 1162261467 | | 151 | 4 | ( 11, 5, 0, 4 ) | 1194891264 | | 152 | 4 | ( 6, 10, 0, 3 ) | 1296243648 | | 153 | 4 | ( 26, 3, 0, 0 ) | 1811939328 | | 154 | 4 | ( 18, 1, 0, 4 ) | 1888223232 | | 155 | 4 | ( 25, 2, 0, 1 ) | 2113929216 | | 156 | 4 | ( 4, 10, 0, 4 ) | 2268426384 | | 157 | 4 | ( 13, 8, 0, 2 ) | 2633637888 | | 158 | 4 | ( 3, 9, 0, 5 ) | 2646497448 | | 159 | 4 | ( 17, 2, 0, 4 ) | 2832334848 | | 160 | 4 | ( 1, 14, 0, 3 ) | 3281116734 | | 161 | 4 | ( 26, 0, 0, 2 ) | 3288334336 | | 162 | 4 | ( 2, 10, 0, 5 ) | 3969746172 | | 163 | 4 | ( 10, 5, 0, 5 ) | 4182119424 | | 164 | 4 | ( 14, 10, 0, 1 ) | 6772211712 | | 165 | 4 | ( 4, 13, 0, 3 ) | 8749644624 | | 166 | 4 | ( 22, 7, 0, 0 ) | 9172942848 | | 167 | 4 | ( 28, 2, 0, 1 ) | 16911433728 | | 168 | 4 | ( 3, 4, 0, 9 ) | 26149137336 | | 169 | 4 | ( 4, 14, 0, 3 ) | 26248933872 | | 170 | 4 | ( 2, 21, 0, 0 ) | 41841412812 | | 171 | 4 | ( 2, 11, 0, 6 ) | 83364669612 | | 172 | 4 | ( 4, 1, 0, 11 ) | 94911683664 | | 173 | 4 | ( 23, 7, 0, 1 ) | 128421199872 | | 174 | 4 | ( 8, 13, 0, 3 ) | 139994313984 | | 175 | 4 | ( 25, 6, 0, 1 ) | 171228266496 | | 176 | 4 | ( 21, 9, 0, 1 ) | 288947699712 | | 177 | 4 | ( 9, 17, 0, 1 ) | 462838344192 | | 178 | 4 | ( 15, 3, 0, 7 ) | 728618139648 | | 179 | 4 | ( 16, 13, 0, 1 ) | 731398864896 | | 180 | 4 | ( 10, 1, 0, 10 ) | 867763964928 | | 181 | 4 | ( 29, 5, 0, 1 ) | 913217421312 | | 182 | 4 | ( 6, 16, 0, 3 ) | 944961619392 | | 183 | 4 | ( 0, 4, 0, 12 ) | 1121144263281 | | 184 | 4 | ( 14, 18, 0, 0 ) | 6347497291776 | | 185 | 4 | ( 2, 17, 0, 5 ) | 8681834878164 | | 186 | 4 | ( 13, 16, 0, 2 ) | 17279298183168 | | 187 | 4 | ( 8, 11, 0, 7 ) | 37347371986176 | | 188 | 4 | ( 0, 9, 0, 11 ) | 38919722282469 | | 189 | 4 | ( 8, 15, 0, 5 ) | 61737492466944 | | 190 | 4 | ( 36, 5, 0, 1 ) | 116891829927936 | | 191 | 4 | ( 31, 3, 0, 4 ) | 139214922448896 | | 192 | 4 | ( 3, 26, 0, 1 ) | 142344486386424 | | 193 | 4 | ( 15, 1, 0, 11 ) | 194379128143872 | | 194 | 4 | ( 10, 15, 0, 5 ) | 246949969867776 | | 195 | 4 | ( 24, 5, 0, 6 ) | 479638912499712 | | 196 | 4 | ( 4, 7, 0, 12 ) | 484334321737392 | | 197 | 4 | ( 0, 10, 0, 12 ) | 817314167931849 | | 198 | 4 | ( 12, 16, 0, 5 ) | 2963399638413312 | | 199 | 4 | ( 2, 26, 0, 3 ) | 3487439916467388 | | 200 | 4 | ( 5, 25, 0, 3 ) | 9299839777246368 | | 201 | 4 | ( 0, 32, 0, 1 ) | 12971141321962887 | | 202 | 4 | ( 7, 16, 0, 8 ) | 31763939874242688 | | 203 | 4 | ( 17, 1, 0, 14 ) | 266688163813392384 | | 204 | 4 | ( 23, 1, 0, 12 ) | 348327397633818624 | | 205 | 4 | ( 9, 27, 0, 3 ) | 1339176927923476992 | | 206 | 4 | ( 55, 2, 0, 1 ) | 2269814212194729984 | | 207 | 4 | ( 0, 22, 0, 10 ) | 8864372626936117641 | | 208 | 4 | ( 30, 21, 0, 0 ) | 11231718727873462272 | | 209 | 4 | ( 31, 12, 0, 5 ) | 19181171229931339776 | | 210 | 4 | ( 47, 11, 0, 0 ) | 24931223849681289216 | | 211 | 4 | ( 9, 4, 0, 19 ) | 472734981127794986496 | | 212 | 4 | ( 59, 5, 0, 2 ) | 6863918177676863471616 |
限于篇幅，仅贴出步数不小于 4 的结果。
大家可以在其中找找看，
是否有两组 value 仅仅是数字 1 的个数有所不同，而其它数字数目完全等同的？ |
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楼主: medie2005
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