Curzon numbers: Difference between revisions

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=={{header|J}}==

A simple test for whether a number is a (generalized) Curzon number is:

<syntaxhighlight lang="j">isCurzon =: 2&$: : (0 = * |&:>: ^)</syntaxhighlight>

Here, the monadic case uses 2 as the left argument for the dyadic case, which handles generalized Curzon numbers.

However, this is inefficient for large numbers, due to it explicitly exponentiating.

Since we test the remainder immediately after, we can use a special combination instead,

<syntaxhighlight lang="j">modpow =: {{ m&|@^ }}

isCurzon =: {{

z =: >: x * y

z = >: x z modpow y

}}</syntaxhighlight>

This avoids performing the large exponentiation, which is significantly faster.

For generating the results:

<syntaxhighlight lang="j">generateCurzons =: {{

found =. i. 0x

current =. 0x

while. 1000 > # found do.

if. y isCurzon current do. found =. found , current end.

current =. >: current

end.

y ; (5 10 $ found) ; {: found

}}

('Base';'First 50';'1000th') , generateCurzons"0 +:>:i.5</syntaxhighlight>

{{out}}

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+----+-------------------------------------------------+------+

|Base|First 50 |1000th|

+----+-------------------------------------------------+------+

|2 | 1 2 5 6 9 14 18 21 26 29 |8646 |

| | 30 33 41 50 53 54 65 69 74 78 | |

| | 81 86 89 90 98 105 113 114 125 134 | |

| |138 141 146 153 158 165 173 174 186 189 | |

| |194 198 209 210 221 230 233 245 249 254 | |

+----+-------------------------------------------------+------+

|4 | 1 3 7 9 13 15 25 27 37 39 |9375 |

| | 43 45 49 57 67 69 73 79 87 93 | |

| | 97 99 105 115 127 135 139 153 163 165 | |

| |169 175 177 183 189 193 199 205 207 213 | |

| |219 235 249 253 255 265 267 273 277 279 | |

+----+-------------------------------------------------+------+

|6 | 1 6 30 58 70 73 90 101 105 121 |20717 |

| |125 146 153 166 170 181 182 185 210 233 | |

| |241 242 266 282 290 322 373 381 385 390 | |

| |397 441 445 446 450 453 530 557 562 585 | |

| |593 601 602 605 606 621 646 653 670 685 | |

+----+-------------------------------------------------+------+

|8 | 1 14 35 44 72 74 77 129 131 137 |22176 |

| |144 149 150 185 200 219 236 266 284 285 | |

| |299 309 336 357 381 386 390 392 402 414 | |

| |420 441 455 459 470 479 500 519 527 536 | |

| |557 582 600 602 617 639 654 674 696 735 | |

+----+-------------------------------------------------+------+

|10 | 1 9 10 25 106 145 190 193 238 253|46845 |

| | 306 318 349 385 402 462 486 526 610 649| |

| | 658 678 733 762 810 990 994 1033 1077 1125| |

| |1126 1141 1149 1230 1405 1422 1441 1485 1509 1510| |

| |1513 1606 1614 1630 1665 1681 1690 1702 1785 1837| |

+----+-------------------------------------------------+------+