・２のべき乗の不思議　　 　 　　　　　　　　 　 　　ＧＡＩ 氏

2^1 × 1 = 2
2^2 × 3 = 12
2^3 × 14 = 112
2^4 × 132 = 2112
2^5 × 691 = 22112
2^6 × 1908 = 122112
2^7 × 16579 = 2122112
2^8 × 47352 = 12122112
2^9 × 414301 = 212122112
2^10 × 1183713 = 1212122112
2^11 × 5474669 = 11212122112
2^12 × 27151397 = 111212122112
2^13 × 135646011 = 1111212122112
2^14 × 678174568 = 11111212122112
2^15 × 6442602909 = 211111212122112
2^16 × 18480090517 = 1211111212122112
2^17 × 85533990571 = 11211111212122112
2^18 × 424236721848 = 111211111212122112
2^19 × 4026815626549 = 2111211111212122112
2^20 × 11550150977337 = 12111211111212122112		 2^1 × 2 = 4
2^2 × 11 = 44
2^3 × 18 = 144
2^4 × 259 = 4144
2^5 × 442 = 14144
2^6 × 6471 = 414144
2^7 × 11048 = 1414144
2^8 × 161774 = 41414144
2^9 × 862137 = 441414144
2^10 × 1407631 = 1441414144
2^11 × 5586628 = 11441414144
2^12 × 100449564 = 411441414144
2^13 × 538506032 = 4411441414144
2^14 × 2710659266 = 44411441414144
2^15 × 13562360883 = 444411441414144
2^16 × 22039969504 = 1444411441414144
2^17 × 316195766002 = 41444411441414144
2^18 × 1683976789251 = 441444411441414144
2^19 × 2749337027438 = 1441444411441414144
2^20 × 39521641169969 = 41441444411441414144
　
2^1 × 3 = 6
2^2 × 4 = 16
2^3 × 77 = 616
2^4 × 101 = 1616
2^5 × 363 = 11616
2^6 × 1744 = 111616
2^7 × 47747 = 6111616
2^8 × 62936 = 16111616
2^9 × 1203343 = 616111616
2^10 × 1578234 = 1616111616
2^11 × 30085992 = 61616111616
2^12 × 161527371 = 661616111616
2^13 × 202833998 = 1661616111616
2^14 × 3763526374 = 61661616111616
2^15 × 20192310062 = 661661616111616
2^16 × 101648889406 = 6661661616111616
2^17 × 508588116578 = 66661661616111616
2^18 × 2543112417664 = 666661661616111616
2^19 × 12715648005707 = 6666661661616111616
2^20 × 15894567166916 = 16666661661616111616		 2^1 × 4 = 8
2^2 × 22 = 88
2^3 × 111 = 888
2^4 × 118 = 1888
2^5 × 2559 = 81888
2^6 × 2842 = 181888
2^7 × 63921 = 8181888
2^8 × 71023 = 18181888
2^9 × 230824 = 118181888
2^10 × 7927912 = 8118181888
2^11 × 43026456 = 88118181888
2^12 × 216825728 = 888118181888
2^13 × 1084975364 = 8888118181888
2^14 × 5425300182 = 88888118181888
2^15 × 27126712591 = 888888118181888
2^16 × 28822145358 = 1888888118181888
2^17 × 624762635179 = 81888888118181888
2^18 × 693851044152 = 181888888118181888
2^19 × 15605714584576 = 8181888888118181888
2^20 × 84096802604788 = 88181888888118181888
　
2^1 × 1 = 2
2^2 × 8 = 32
2^3 × 29 = 232
2^4 × 202 = 3232
2^5 × 726 = 23232
2^6 × 3488 = 223232
2^7 × 17369 = 2223232
2^8 × 125872 = 32223232
2^9 × 453561 = 232223232
2^10 × 3156468 = 3232223232
2^11 × 11343859 = 23232223232
2^12 × 78914117 = 323232223232
2^13 × 405667996 = 3323232223232
2^14 × 1423537123 = 23323232223232
2^15 × 9867041999 = 323323232223232
2^16 × 50709888187 = 3323323232223232
2^17 × 254236780031 = 33323323232223232
2^18 × 1271527569703 = 333323323232223232
2^19 × 6357809683289 = 3333323323232223232
2^20 × 31789134333832 = 33333323323232223232		 2^1 × 2 = 4
2^2 × 11 = 44
2^3 × 43 = 344
2^4 × 209 = 3344
2^5 × 1042 = 33344
2^6 × 6771 = 433344
2^7 × 26823 = 3433344
2^8 × 130599 = 33433344
2^9 × 651237 = 333433344
2^10 × 3255306 = 3333433344
2^11 × 21158903 = 43333433344
2^12 × 83821639 = 343333433344
2^13 × 408121757 = 3343333433344
2^14 × 2035115566 = 33343333433344
2^15 × 13224589033 = 433343333433344
2^16 × 52388661704 = 3433343333433344
2^17 × 331370112102 = 43433343333433344
2^18 × 1691563962301 = 443433343333433344
2^19 × 6567827879588 = 3443433343333433344
2^20 × 41430886596044 = 43443433343333433344
　
2^1 × 3 = 6
2^2 × 9 = 36
2^3 × 42 = 336
2^4 × 396 = 6336
2^5 × 2073 = 66336
2^6 × 5724 = 366336
2^7 × 49737 = 6366336
2^8 × 142056 = 36366336
2^9 × 1242903 = 636366336
2^10 × 3551139 = 3636366336
2^11 × 16424007 = 33636366336
2^12 × 81454191 = 333636366336
2^13 × 406938033 = 3333636366336
2^14 × 2034523704 = 33333636366336
2^15 × 19327808727 = 633333636366336
2^16 × 55440271551 = 3633333636366336
2^17 × 256601971713 = 33633333636366336
2^18 × 1272710165544 = 333633333636366336
2^19 × 12080446879647 = 6333633333636366336
2^20 × 34650452932011 = 36333633333636366336		 2^1 × 4 = 8
2^2 × 22 = 88
2^3 × 111 = 888
2^4 × 243 = 3888
2^5 × 1059 = 33888
2^6 × 5217 = 333888
2^7 × 26046 = 3333888
2^8 × 325523 = 83333888
2^9 × 748699 = 383333888
2^10 × 3304037 = 3383333888
2^11 × 16300456 = 33383333888
2^12 × 203462728 = 833383333888
2^13 × 1078293864 = 8833383333888
2^14 × 5421959432 = 88833383333888
2^15 × 27125042216 = 888833383333888
2^16 × 135632833608 = 8888833383333888
2^17 × 678167979304 = 88888833383333888
2^18 × 3390841802152 = 888888833383333888
2^19 × 16954209963576 = 8888888833383333888
2^20 × 84771050294288 = 88888888833383333888
　
2^1 × 1 = 2
2^2 × 13 = 52
2^3 × 69 = 552
2^4 × 347 = 5552
2^5 × 1736 = 55552
2^6 × 3993 = 255552
2^7 × 41059 = 5255552
2^8 × 215842 = 55255552
2^9 × 498546 = 255255552
2^10 × 2202398 = 2255255552
2^11 × 10866824 = 22255255552
2^12 × 54261537 = 222255255552
2^13 × 637482331 = 5222255255552
2^14 × 3370498978 = 55222255255552
2^15 × 7788765114 = 255222255255552
2^16 × 34411960682 = 2255222255255552
2^17 × 169793870966 = 22255222255255552
2^18 × 847836388608 = 222255222255255552
2^19 × 4238615459929 = 2222255222255255552
2^20 × 49803023550277 = 52222255222255255552		 2^1 × 2 = 4
2^2 × 11 = 44
2^3 × 68 = 544
2^4 × 284 = 4544
2^5 × 1392 = 44544
2^6 × 6946 = 444544
2^7 × 34723 = 4444544
2^8 × 212674 = 54444544
2^9 × 887587 = 454444544
2^10 × 5326606 = 5454444544
2^11 × 22194553 = 45454444544
2^12 × 133167589 = 545454444544
2^13 × 676935357 = 5545454444544
2^14 × 3390225491 = 55545454444544
2^15 × 16953901808 = 555545454444544
2^16 × 69512107154 = 4555545454444544
2^17 × 339931834827 = 44555545454444544
2^18 × 2077314550226 = 544555545454444544
2^19 × 8668051806363 = 4544555545454444544
2^20 × 52017741723494 = 54544555545454444544
　
2^1 × 3 = 6
2^2 × 14 = 56
2^3 × 82 = 656
2^4 × 416 = 6656
2^5 × 2083 = 66656
2^6 × 8854 = 566656
2^7 × 51302 = 6566656
2^8 × 260026 = 66566656
2^9 × 1301888 = 666566656
2^10 × 6510319 = 6666566656
2^11 × 27669222 = 56666566656
2^12 × 160318986 = 656666566656
2^13 × 812581368 = 6656666566656
2^14 × 4068400059 = 66656666566656
2^15 × 17292989092 = 566656666566656
2^16 × 100199228921 = 6566656666566656
2^17 × 431569341023 = 56566656666566656
2^18 × 2123133303324 = 556566656666566656
2^19 × 12505658448537 = 6556566656666566656
2^20 × 53936545044581 = 56556566656666566656		 2^1 × 4 = 8
2^2 × 22 = 88
2^3 × 111 = 888
2^4 × 368 = 5888
2^5 × 2684 = 85888
2^6 × 13842 = 885888
2^7 × 69421 = 8885888
2^8 × 230023 = 58885888
2^9 × 1091574 = 558885888
2^10 × 8358287 = 8558885888
2^11 × 28593206 = 58558885888
2^12 × 209609103 = 858558885888
2^13 × 715156114 = 5858558885888
2^14 × 5240390557 = 85858558885888
2^15 × 17878984341 = 585858558885888
2^16 × 85233437483 = 5585858558885888
2^17 × 424086445304 = 55585858558885888
2^18 × 3263801035152 = 855585858558885888
2^19 × 16890689580076 = 8855585858558885888
2^20 × 84739290102538 = 88855585858558885888
　
2^1 × 1 = 2
2^2 × 18 = 72
2^3 × 34 = 272
2^4 × 142 = 2272
2^5 × 696 = 22272
2^6 × 3473 = 222272
2^7 × 56424 = 7222272
2^8 × 106337 = 27222272
2^9 × 1420356 = 727222272
2^10 × 2663303 = 2727222272
2^11 × 35511339 = 72727222272
2^12 × 188654107 = 772727222272
2^13 × 948819241 = 7772727222272
2^14 × 4746870558 = 77772727222272
2^15 × 8476950904 = 277772727222272
2^16 × 34756053577 = 2277772727222272
2^17 × 551435643976 = 72277772727222272
2^18 × 1038657275113 = 272277772727222272
2^19 × 13870769067244 = 7272277772727222272
2^20 × 26008870861747 = 27272277772727222272		 2^1 × 2 = 4
2^2 × 11 = 44
2^3 × 93 = 744
2^4 × 484 = 7744
2^5 × 1492 = 47744
2^6 × 6996 = 447744
2^7 × 34748 = 4447744
2^8 × 173624 = 44447744
2^9 × 868062 = 444447744
2^10 × 4340281 = 4444447744
2^11 × 36349828 = 74444447744
2^12 × 115831164 = 474444447744
2^13 × 546196832 = 4474444447744
2^14 × 2714504666 = 44474444447744
2^15 × 13564283583 = 444474444447744
2^16 × 113593665229 = 7444474444447744
2^17 × 590854449802 = 77444474444447744
2^18 × 1821306131151 = 477444474444447744
2^19 × 14262093495263 = 7477444474444447744
2^20 × 73888248896069 = 77477444474444447744
　
2^1 × 3 = 6
2^2 × 19 = 76
2^3 × 97 = 776
2^4 × 486 = 7776
2^5 × 2118 = 67776
2^6 × 10434 = 667776
2^7 × 52092 = 6667776
2^8 × 260421 = 66667776
2^9 × 1497398 = 766667776
2^10 × 6608074 = 6766667776
2^11 × 32600912 = 66766667776
2^12 × 162784831 = 666766667776
2^13 × 935884603 = 7666766667776
2^14 × 4740403239 = 77666766667776
2^15 × 23732506307 = 777666766667776
2^16 × 118677776591 = 7777666766667776
2^17 × 593396505483 = 77777666766667776
2^18 × 2966986338679 = 777777666766667776
2^19 × 14834933599027 = 7777777666766667776
2^20 × 74174668947951 = 77777777666766667776		 2^1 × 4 = 8
2^2 × 22 = 88
2^3 × 111 = 888
2^4 × 493 = 7888
2^5 × 2434 = 77888
2^6 × 13717 = 877888
2^7 × 61546 = 7877888
2^8 × 343273 = 87877888
2^9 × 1538824 = 787877888
2^10 × 8581912 = 8787877888
2^11 × 43353456 = 88787877888
2^12 × 216989228 = 888787877888
2^13 × 1085057114 = 8888787877888
2^14 × 5425341057 = 88888787877888
2^15 × 24074975216 = 788888787877888
2^16 × 134107800108 = 8788888787877888
2^17 × 677405462554 = 88788888787877888
2^18 × 3390460543777 = 888788888787877888
2^19 × 15046670701576 = 7888788888787877888
2^20 × 83817280663288 = 87888788888787877888
　
2^1 × 1 = 2
2^2 × 23 = 92
2^3 × 124 = 992
2^4 × 187 = 2992
2^5 × 2906 = 92992
2^6 × 4578 = 292992
2^7 × 17914 = 2292992
2^8 × 87082 = 22292992
2^9 × 434166 = 222292992
2^10 × 2170208 = 2222292992
2^11 × 10850729 = 22222292992
2^12 × 225151927 = 922222292992
2^13 × 1211208776 = 9922222292992
2^14 × 1826307513 = 29922222292992
2^15 × 28378974069 = 929922222292992
2^16 × 151518588597 = 9929922222292992
2^17 × 762404802111 = 99929922222292992
2^18 × 3814429940118 = 999929922222292992
2^19 × 5721912235684 = 2999929922222292992
2^20 × 21934442445967 = 22999929922222292992		 2^1 × 2 = 4
2^2 × 11 = 44
2^3 × 118 = 944
2^4 × 309 = 4944
2^5 × 2967 = 94944
2^6 × 15546 = 994944
2^7 × 39023 = 4994944
2^8 × 371074 = 94994944
2^9 × 966787 = 494994944
2^10 × 9272456 = 9494994944
2^11 × 24167478 = 49494994944
2^12 × 109739989 = 449494994944
2^13 × 1153502807 = 9449494994944
2^14 × 6069915466 = 99449494994944
2^15 × 15241988983 = 499449494994944
2^16 × 144950096054 = 9499449494994944
2^17 × 377650829277 = 49499449494994944
2^18 × 3622052953701 = 949499449494994944
2^19 × 18977164172163 = 9949499449494994944
2^20 × 95319270562644 = 99949499449494994944
　
2^1 × 3 = 6
2^2 × 24 = 96
2^3 × 87 = 696
2^4 × 606 = 9696
2^5 × 2178 = 69696
2^6 × 10464 = 669696
2^7 × 52107 = 6669696
2^8 × 377616 = 96669696
2^9 × 1360683 = 696669696
2^10 × 9469404 = 9696669696
2^11 × 34031577 = 69696669696
2^12 × 236742351 = 969696669696
2^13 × 1217003988 = 9969696669696
2^14 × 4270611369 = 69969696669696
2^15 × 29601125997 = 969969696669696
2^16 × 152129664561 = 9969969696669696
2^17 × 762710340093 = 99969969696669696
2^18 × 3814582709109 = 999969969696669696
2^19 × 19073429049867 = 9999969969696669696
2^20 × 95367403001496 = 99999969969696669696		 2^1 × 4 = 8
2^2 × 22 = 88
2^3 × 111 = 888
2^4 × 618 = 9888
2^5 × 2809 = 89888
2^6 × 15467 = 989888
2^7 × 78046 = 9989888
2^8 × 351523 = 89989888
2^9 × 1933574 = 989989888
2^10 × 8779287 = 8989989888
2^11 × 48334956 = 98989989888
2^12 × 219479978 = 898989989888
2^13 × 1086302489 = 8898989989888
2^14 × 6036315307 = 98898989989888
2^15 × 30483977966 = 998898989989888
2^16 × 137312301483 = 8998898989989888
2^17 × 755301658554 = 98998898989989888
2^18 × 3429408641777 = 898998898989989888
2^19 × 18880842016201 = 9898998898989989888
2^20 × 95271109484663 = 99898998898989989888


　空舟さんからのコメントです。（平成２５年１月２７日付け）

　2^4*A=4144　であるとき、14144 = 2^4*(5^4+A) と 44144 = 2^4*(4*5^4+A)　のどちらかは
2^5で割り切れる。という理屈ですね・・・。[(5^4+A)と(4*5^4+259) のどちらかは偶数だから]



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