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| -rw-r--r-- | challenge-169/james-smith/README.md | 94 |
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diff --git a/challenge-169/james-smith/README.md b/challenge-169/james-smith/README.md index 4be886eb18..67ec30184d 100644 --- a/challenge-169/james-smith/README.md +++ b/challenge-169/james-smith/README.md @@ -97,42 +97,7 @@ The output in each row is the brilliant number and the two primes which are it's 50: 713 = 23 x 31 ``` -For large `n` we have: -``` - 100: 21,600 = 2^5 . 3^3 . 5^2 - 200: 66,248 = 2^3 . 7^2 . 13^2 - 300: 136,107 = 3^3 . 71^2 - 400: 225,000 = 2^3 . 3^2 . 5^5 - 500: 333,396 = 2^2 . 3^5 . 7^3 - 600: 464,648 = 2^3 . 241^2 - 700: 617,400 = 2^3 . 3^2 . 5^2 . 7^3 - 800: 784,000 = 2^7 . 5^3 . 7^2 - 900: 969,624 = 2^3 . 3^3 . 67^2 - 1000: 1,179,648 = 2^17 . 3^2 - 2000: 4,255,443 = 3^3 . 397^2 - 3000: 9,082,800 = 2^4 . 3^3 . 5^2 . 29^2 - 4000: 15,635,232 = 2^5 . 3^2 . 233^2 - 5000: 23,876,179 = 19^3 . 59^2 - 6000: 33,818,428 = 2^2 . 7^3 . 157^2 - 7000: 45,489,708 = 2^2 . 3^3 . 11^2 . 59^2 - 8000: 58,752,800 = 2^5 . 5^2 . 271^2 - 9000: 73,641,248 = 2^5 . 37^2 . 41^2 - 10000: 90,209,312 = 2^5 . 23^2 . 73^2 - 20000: 344,478,752 = 2^5 . 17^2 . 193^2 - 30000: 758,595,456 = 2^7 . 3^5 . 29^3 - 40000: 1,330,259,301 = 3^3 . 7^3 . 379^2 - 50000: 2,057,748,300 = 2^2 . 3^7 . 5^2 . 97^2 - 60000: 2,941,077,600 = 2^5 . 3^7 . 5^2 . 41^2 - 70000: 3,978,593,667 = 3^3 . 61^2 . 199^2 - 80000: 5,171,352,984 = 2^3 . 3^5 . 7^2 . 233^2 - 90000: 6,518,604,456 = 2^3 . 3^2 . 7^2 . 13^3 . 29^2 -100000: 8,017,975,944 = 2^3 . 3^3 . 11^3 . 167^2 -150000: 17,810,638,848 = 2^11 . 3^2 . 983^2 -200000: 31,413,171,744 = 2^5 . 3^2 . 17^3 . 149^2 -250000: 48,804,377,888 = 2^5 . 7^4 . 797^2 -300000: 69,976,609,587 = 3^3 . 50909^2 -``` ### Removing pretty print If we remove the pretty print this reduces to: @@ -226,8 +191,67 @@ The following are the first 50 achilles numbers. 49: 6912 = 2^8 . 3^3 50: 7200 = 2^5 . 3^2 . 5^2 ``` + +Some examples for larger values of `n` are: + +| Index | Value | Factors | +| -----------: | -------------------: | ------------------------------------------------------------ | +| 100 | 21,600 | 2<sup>5</sup>.3<sup>3</sup>.5<sup>2</sup> | +| 200 | 66,248 | 2<sup>3</sup>.7<sup>2</sup>.13<sup>2</sup> | +| 300 | 136,107 | 3<sup>3</sup>.71<sup>2</sup> | +| 400 | 225,000 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>5</sup> | +| 500 | 333,396 | 2<sup>2</sup>.3<sup>5</sup>.7<sup>3</sup> | +| 600 | 464,648 | 2<sup>3</sup>.241<sup>2</sup> | +| 700 | 617,400 | 2<sup>3</sup>.3<sup>2</sup>.5<sup>2</sup>.7<sup>3</sup> | +| 800 | 784,000 | 2<sup>7</sup>.5<sup>3</sup>.7<sup>2</sup> | +| 900 | 969,624 | 2<sup>3</sup>.3<sup>3</sup>.67<sup>2</sup> | +| 1,000 | 1,179,648 | 2<sup>17</sup>.3<sup>2</sup> | +| 2,000 | 4,255,443 | 3<sup>3</sup>.397<sup>2</sup> | +| 3,000 | 9,082,800 | 2<sup>4</sup>.3<sup>3</sup>.5<sup>2</sup>.29<sup>2</sup> | +| 4,000 | 15,635,232 | 2<sup>5</sup>.3<sup>2</sup>.233<sup>2</sup> | +| 5,000 | 23,876,179 | 19<sup>3</sup>.59<sup>2</sup> | +| 6,000 | 33,818,428 | 2<sup>2</sup>.7<sup>3</sup>.157<sup>2</sup> | +| 7,000 | 45,489,708 | 2<sup>2</sup>.3<sup>3</sup>.11<sup>2</sup>.59<sup>2</sup> | +| 8,000 | 58,752,800 | 2<sup>5</sup>.5<sup>2</sup>.271<sup>2</sup> | +| 9,000 | 73,641,248 | 2<sup>5</sup>.37<sup>2</sup>.41<sup>2</sup> | +| 10,000 | 90,209,312 | 2<sup>5</sup>.23<sup>2</sup>.73<sup>2</sup> | +| 20,000 | 344,478,752 | 2<sup>5</sup>.17<sup>2</sup>.193<sup>2</sup> | +| 30,000 | 758,595,456 | 2<sup>7</sup>.3<sup>5</sup>.29<sup>3</sup> | +| 40,000 | 1,330,259,301 | 3<sup>3</sup>.7<sup>3</sup>.379<sup>2</sup> | +| 50,000 | 2,057,748,300 | 2<sup>2</sup>.3<sup>7</sup>.5<sup>2</sup>.97<sup>2</sup> | +| 60,000 | 2,941,077,600 | 2<sup>5</sup>.3<sup>7</sup>.5<sup>2</sup>.41<sup>2</sup> | +| 70,000 | 3,978,593,667 | 3<sup>3</sup>.61<sup>2</sup>.199<sup>2</sup> | +| 80,000 | 5,171,352,984 | 2<sup>3</sup>.3<sup>5</sup>.7<sup>2</sup>.233<sup>2</sup> | +| 90,000 | 6,518,604,456 | 2<sup>3</sup>.3<sup>2</sup>.7<sup>2</sup>.13<sup>3</sup>.29<sup>2</sup> | +| 100,000 | 8,017,975,944 | 2<sup>3</sup>.3<sup>3</sup>.11<sup>3</sup>.167<sup>2</sup> | +| 125,000 | 12,437,566,904 | 2<sup>3</sup>.7<sup>3</sup>.2129<sup>2</sup> | +| 150,000 | 17,810,638,848 | 2<sup>11</sup>.3<sup>2</sup>.983<sup>2</sup> | +| 175,000 | 24,140,196,992 | 2<sup>7</sup>.31<sup>2</sup>.443<sup>2</sup> | +| 200,000 | 31,413,171,744 | 2<sup>5</sup>.3<sup>2</sup>.17<sup>3</sup>.149<sup>2</sup> | +| 225,000 | 39,636,156,125 | 5<sup>3</sup>.17807<sup>2</sup> | +| 250,000 | 48,804,377,888 | 2<sup>5</sup>.7<sup>4</sup>.797<sup>2</sup> | +| 275,000 | 58,919,206,088 | 2<sup>3</sup>.85819<sup>2</sup> | +| 300,000 | 69,976,609,587 | 3<sup>3</sup>.50909<sup>2</sup> | +| 325,000 | 81,981,196,443 | 3<sup>3</sup>.55103<sup>2</sup> | + +And these are the first numbers with `n` digits... + +| Index | Value | Factors | +| -----------: | -------------------: | ------------------------------------------------------------ | +| 1 | 72 | 2<sup>3</sup>.3<sup>2</sup> | +| 2 | 108 | 2<sup>2</sup>.3<sup>3</sup> | +| 14 | 1,125 | 3<sup>2</sup>.5<sup>3</sup> | +| 61 | 10,125 | 3<sup>4</sup>.5<sup>3</sup> | +| 253 | 100,352 | 2<sup>11</sup>.7<sup>2</sup> | +| 917 | 1,000,188 | 2<sup>2</sup>.3<sup>6</sup>.7<sup>3</sup> | +| 3,159 | 10,011,125 | 5<sup>3</sup>.283<sup>2</sup> | +| 10,554 | 100,018,800 | 2<sup>4</sup>.3<sup>6</sup>.5<sup>2</sup>.7<sup>3</sup> | +| 34,562 | 1,000,042,200 | 2<sup>3</sup>.3<sup>6</sup>.5<sup>2</sup>.19<sup>3</sup> | +| 111,892 | 10,000,373,888 | 2<sup>7</sup>.8839<sup>2</sup> | + ### Removing pretty print + If we remove the pretty print this reduces to: ```perl |