Talk:Minimum positive multiple in base 10 using only 0 and 1: Difference between revisions
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:: Yuppers, I wrongedlyness bidirectionally confuseducated '''B10''' with the multiplier. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 23:43, 2 March 2020 (UTC) |
:: Yuppers, I wrongedlyness bidirectionally confuseducated '''B10''' with the multiplier. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 23:43, 2 March 2020 (UTC) |
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::: I think about prime decomposition of the integer to test, because of the observation that 3 is equivilant to 37 both are factors of 111, so when a number has a factor of 37 I can substitute it by 3, like 2 and 5 both are the factors of 10.<BR>But this is only possible, when both numbers are prime.<BR>7 and 143= 11*13 with 7*(11*13) =1001 so 143*37 = 5291 can't be transformed to 3*7 = 21 with the same result,but into 143*3. |
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<pre style="height:150px"> |
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B10(21) 10101 : 3[ 111]*7[ 1001] |
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B10(5291) 111111 : 11[ 11]*13[ 1001]*37[ 111] // substitute 37 with 3 |
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B10(429) 111111 : 3[ 111]*11[ 11]*13[ 1001] |
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prime combinations found til 100,000 factor2 can be substituted by factor1 |
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factor1 factor2 B10(factor1) B10(factor2) |
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2 5 10 10 |
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3 37 111 111 |
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17 653 11101 11101 |
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23 4787 110101 110101 |
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31 3581 111011 111011 |
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41 271 11111 11111 |
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59 186629 11011111 11011111 |
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67 16433 1101011 1101011 |
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73 137 10001 10001 |
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83 1217 101011 101011 |
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107 934673 100010011 100010011 |
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127 86693 11010011 11010011 |
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149 739 110111 110111 |
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151 7351 1110001 1110001 |
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163 6197 1010111 1010111 |
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167 66533 11111011 11111011 |
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181 5531 1001111 1001111 |
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199 557789 111000011 111000011 |
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227 48463 11001101 11001101 |
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239 4649 1111111 1111111 |
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241 461 111101 111101 |
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311 324791 101010001 101010001 |
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331 335381 111011111 111011111 |
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397 27733 11010001 11010001 |
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419 23869 10001111 10001111 |
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421 237791 100110011 100110011 |
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431 234571 101100101 101100101 |
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449 247439 111100111 111100111 |
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457 2190593 1001101001 1001101001 |
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467 214133 100000111 100000111 |
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487 2258953 1100110111 1100110111 |
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521 1938791 1010110111 1010110111 |
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541 18671 10101011 10101011 |
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557 1993 1110101 1110101 |
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587 17053 10010111 10010111 |
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617 1783 1100111 1100111 |
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631 160081 101011111 101011111 |
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881 113621 100100101 100100101 |
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929 1184069 1100000101 1100000101 |
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971 1031 1001101 1001101 |
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1097 1012763 1111001011 1111001011 |
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1123 89057 100011011 100011011 |
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1381 724121 1000011101 1000011101 |
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1511 6691 10110101 10110101 |
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1559 706229 1101011011 1101011011 |
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1567 638233 1000111111 1000111111 |
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1601 69401 111111001 111111001 |
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1777 56843 101010011 101010011 |
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1823 608887 1110001001 1110001001 |
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1949 564449 1100111101 1100111101 |
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2293 480157 1101000001 1101000001 |
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3109 321679 1000100011 1000100011 |
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3313 335077 1110110101 1110110101 |
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3371 299941 1011101111 1011101111 |
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3407 293543 1000101001 1000101001 |
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3461 292141 1011100001 1011100001 |
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3593 306457 1101100001 1101100001 |
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3761 268841 1011111001 1011111001 |
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3889 25999 101110111 101110111 |
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5557 19993 111101101 111101101 |
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6131 179581 1101011111 1101011111 |
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6949 14549 101101001 101101001 |
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6971 145031 1011011101 1011011101 |
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7411 149791 1110101101 1110101101 |
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7573 13337 101001101 101001101 |
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7757 12893 100011001 100011001 |
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7937 13873 110110001 110110001 |
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9199 119699 1101111101 1101111101 |
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9391 11821 111011011 111011011 |
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9829 102859 1011001111 1011001111 |
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9833 11197 110100101 110100101 |
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12589 80309 1011010001 1011010001 |
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25147 43783 1101011101 1101011101 |
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25913 38977 1010011001 1010011001 |
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27739 39659 1100101001 1100101001 |
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30241 33071 1000100111 1000100111</pre> |
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so a factor 934673 can substituted by 107, much less work to be done.But very seldom. |
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For very long B10 3/37 and 41/271 are often factors. |
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--[[user Horst.h|Horst.h]] 11:21, 3 March 2020 (UTC)~ |