Numbers

Oh well, another lame “project” by the boliao JH. Hehe, you guys can contribute if you want, I won’t mind. =D I’ll see how far I can go. Yes, I will try to do in numerical order, starting from 1. Probably will be abandoned/left alone after some time. Lol.

I know this can probably be programmed out by some of you out there, but hey I find more joy in finding my own combinations :P

Conditions to self: use not more than 4 operators (yes I’m lenient on myself).

1 to 300

1 = 3² – 2³ 2 = 3³ – 5² 3 = 27 – 5³
4 = 2² 5 = 25 – 3³ 6 = 2² + 3³ – 5²
7 = 4² – 3² 8 = 2³ 9 = 3²
10 = 17² – 21² + 11² 11 = 6² – 5² 12 = 2² + 2³
13 = 16² – 35 14 = 6³ – 11² – 9² 15 = 35 – 27 – 10²
16 = 4² 17 = 5² – 2³ 18 = 6² + 3² – 3³
19 = 10² – 9² 20 = 4² + 2² 21 = 5² – 2²
22 = 7² – 3³ 23 = 25 – 3² 24 = 7² – 5²
25 = 5² 26 = 5² + 3² – 2³ 27 = 3³
28 = 25 – 2² 29 = 5² + 2² 30 = 8² – 5² – 3²
31 = 25 + 2³ – 3² 32 = 25 33 = 17² – 16²
34 = 5² + 3² 35 = 6² + 2³ – 3² 36 = 6²
37 = 6² – 2³ + 3² 38 = 7³ – 35 – 4² 39 = 8² – 5²
40 = 6² + 2² 41 = 25 + 3² 42 = 23² – 8³ + 5²
43 = 35 – 14² – 2² 44 = 6² + 2³ 45 = 6² + 3²
46 = 17² – 35 47 = 27 – 9² 48 = 25 + 4²
49 = 7² 50 = 5² + 5² 51 = 10² – 7²
52 = 6² + 4² 53 = 12² – 3³ – 8² 54 = 3³ + 3³
55 = 8³ – 3³ 56 = 8² – 2³ 57 = 25 + 5²
58 = 35 – 11² – 8² 59 = 6³ – 11² – 6² 60 = 8² – 2²
61 = 5³ – 8² 62 = 20² – 17² – 7² 63 = 3³ + 6²
64 = 8² 65 = 7² + 4² 66 = 20² – 7³ + 3²
67 = 35 – 12² – 25 68 = 8² + 2² 69 = 13² – 10²
70 = 27 – 7² – 3² 71 = 27 – 7² – 2³ 72 = 11² – 7²
73 = 8² + 3² 74 = 7² + 5² 75 = 10² – 5²
76 = 5³ – 7² 77 = 9² – 2² 78 = 7² + 5² + 2²
79 = 27 – 7² 80 = 4³ + 4² 81 = 9²
82 = 9² + 3² – 2³ 83 = 7² + 5² + 3² 84 = 10² – 4²
85 = 9² + 2² 86 = 19² – 35 – 25 87 = 6³ – 11² – 2³
88 = 23² – 21² 89 = 8² + 5² 90 = 9² + 3²
91 = 10² – 3² 92 = 10² – 2³ 93 = 17² – 14²
94 = 11² – 3³ 95 = 6³ – 11² 96 = 26 + 25
97 = 9³ + 4² 98 = 5³ – 3³ 99 = 2² * 3³ – 3²
100 = 10² 101 = 27 – 3³ 102 = 7³ – 6³ – 5²
103 = 18² – 10² – 11² 104 = 10² + 2² 105 = 13² – 8²
106 = 18² – 13² – 7² 107 = 10² + 4² – 3² 108 = 10² + 2³
109 = 10² + 3² 110 = 5² + 9² + 2² 111 = 20² – 17²
112 = 10² + 2² + 2³ 113 = 10² + 16² – 35 114 = 8² + 5² + 5²
115 = 35 – 27 116 = 10² + 4² 117 = 11² – 2²
118 = 7³ – 5³ – 10² 119 = 27 – 3² 120 = 27 – 2³
121 = 11² 122 = 11² + 3² – 2² 123 = 10² + 25 – 3²
124 = 27 – 2² 125 = 5³ 126 = 5³ + 3² – 2³
127 = 10² + 3³ 128 = 27 129 = 5³ + 2²
130 = 18² – 13² – 5² 131 = 18² – 12² – 7² 132 = 27 + 2²
133 = 5³ + 2³ 134 = 5³ + 3² 135 = 24² – 21²
136 = 27 + 2³ 137 = 27 + 3² 138 = 7³ – 6² – 13²
139 = 18² – 13² – 4² 140 = 12² – 2² 141 = 16² – 35 + 27
142 = 13² – 3³ 143 = 12² + 2³ – 3² 144 = 12²
145 = 12² + 3² – 2³ 146 = 11² + 5² 147 = 10² + 27 – 9²
148 = 12² + 2² 149 = 10² + 7² 150 = 10² + 5² + 5²
151 = 8³ – 19² 152 = 12² + 2³ 153 = 12² + 3²
154 = 35 + 25 – 11² 155 = 27 + 3³ 156 = 16² – 15² + 5³
157 = 11² + 6² 158 = 35 + 6² – 11² 159 = 16² – 15² + 27
160 = 13² – 3² 161 = 13² – 2³ 162 = 35 – 9²
163 = 7³ – 6² – 12² 164 = 10² + 8² 165 = 13² – 2²
166 = 13² – 27 – 5³ 167 = 14² – 2² – 5² 168 = 13² + 2³ – 3²
169 = 13² 170 = 11² + 7² 171 = 12² + 3³
172 = 14² + 2³ – 25 173 = 13² + 2² 174 = 17² – 35 + 27
175 = 20² – 15² 176 = 21² – 12² – 11² 177 = 13² + 2³
178 = 13² + 3² 179 = 35 – 8² 180 = 12² + 6²
181 = 10² + 9² 182 = 13² + 2² + 3² 183 = 14² + 6² – 7²
184 = 10² + 10² – 4² 185 = 11² + 8² 186 = 7³ – 6² – 11²
187 = 14² – 3² 188 = 14² – 2³ 189 = 10² + 8² + 5²
190 = 10² + 9² + 3² 191 = 7³ – 6³ + 8² 192 = 14² – 2²
193 = 12² + 7² 194 = 35 + 25 – 9² 195 = 14² – 3² + 2²
196 = 14² 197 = 14² – 2³ + 3² 198 = 21² – 35
199 = 18² – 5³ 200 = 2³ * 5² 201 = 10² + 27 – 3³
202 = 11² + 9² 203 = 18² – 11² 204 = 14² + 2²
205 = 14² + 3² 206 = 15² + 2³ – 3³ 207 = 6³ – 3²
208 = 6³ – 2³ 209 = 15² – 4² 210 = 11² + 8² + 5²
211 = 11² + 10² 212 = 14² + 4² 213 = 16² – 4² – 3³
214 = 15² + 5² – 6² 215 = 7³ – 27 216 = 6³
217 = 15² – 2³ 218 = 35 – 5² 219 = 20² – 10² – 9²
220 = 6³ + 2² 221 = 15² – 2² 222 = 7³ – 11²
223 = 35 – 4² – 2² 224 = 6³ + 2³ 225 = 15²
226 = 11² + 13² – 8² 227 = 35 – 4² 228 = 14² + 25
229 = 15² + 2² 230 = 35 – 2² – 3² 231 = 16² – 5²
232 = 14² + 6² 233 = 15² + 2³ 234 = 15² + 3²
235 = 35 – 2³ 236 = 19² – 5³ 237 = 15² + 2³ + 2²
238 = 11² + 11² – 2² 239 = 35 – 2² 240 = 16² – 4²
241 = 11² + 13² – 7² 242 = 11² + 11² 243 = 35
244 = 12² + 10² 245 = 14² + 7² 246 = 11² + 11² + 2²
247 = 16² – 3² 248 = 16² – 2³ 249 = 14² + 7² + 2²
250 = 15² + 5² 251 = 35 + 2³ 252 = 16² – 2²
253 = 7³ – 9² – 3² 254 = 11² + 13² – 6² 255 = 16² + 2³ – 3²
256 = 16² 257 = 17² + 2² – 6² 258 = 11² + 13² – 25
259 = 35 + 4² 260 = 16² + 2² 261 = 15² + 6²
262 = 7³ – 9² 263 = 18² – 5² – 6² 264 = 16² + 2³
265 = 16² + 3² 266 = 18² – 7² – 3² 267 = 18² – 7² – 2³
268 = 35 + 5² 269 = 13² + 10² 270 = 35 + 3³
271 = 18² – 7² – 2² 272 = 16² + 4² 273 = 16² + 5² – 2³
274 = 15² + 7² 275 = 18² – 7² 276 = 26² – 20²
277 = 14² + 9² 278 = 7³ – 7² – 4² 279 = 35 + 6²
280 = 19² – 9² 281 = 16² + 5² 282 = 11² + 13² – 2³
283 = 18² – 5² – 4² 284 = 20² – 10² – 4² 285 = 17² – 2²
286 = 11² + 13² – 2² 287 = 16² + 2² + 3³ 288 = 12² + 12²
289 = 17² 290 = 11² + 13² 291 = 20² – 10² – 3²
292 = 35 + 7² 293 = 17² + 2² 294 = 7³ – 7²
295 = 18² – 5² – 2² 296 = 14² + 10² 297 = 17² + 2³
298 = 17² + 3² 299 = 18² – 5² 300 = 20² – 10²
301 = 17² + 2³ + 2² 302 = 17² + 3² + 2² 303 = 7³ – 6² – 2²
304 = 20² – 10² +2² 305 = 17² + 4² 306 = 17² + 2³ + 3²
307 = 7³ – 6² 308 = 18² – 4² 309 = 7³ – 5² – 3²
310 = 17² + 5² – 2² 311 = 7³ – 6² + 2² 312 = 19² – 7²
313 = 17² + 2³ + 4² 314 = 17² + 5² 315 = 18² – 3²
316 = 18² – 2³ 317 = 18² – 4² + 3² 318 = 7³ – 5²
319 = 20² – 9² 320 = 18² – 2² 321 = 19² – 7² + 3²
322 = 17² + 7² – 4² 323 = 20² – 9² + 2² 324 = 18²
325 = 17² + 6² 326 = 7³ – 3² – 2³ 327 = 7³ – 4²
328 = 18² + 2² 329 = 18² – 2² + 3² 330 = 7³ – 3² – 2²
331 = 7³ – 2³ – 2² 332 = 18² + 2³ 333 = 18² + 3²
334 = 7³ – 3² 335 = 7³ – 2³ 336 = 20² – 8²
337 = 18² + 2² + 3² 338 = 17² + 7² 339 = 7³ – 2²
340 = 18² + 5² – 3² 341 = 19² – 5² – 2² 342 = 20² – 3² – 7²
343 = 7³ 344 = 7³ – 2³ + 3² 345 = 19² – 5²
346 = 17² + 2³ + 7² 347 = 7³ + 2² 348 = 7³ + 3² – 2²
349 = 18² + 5² 350 = 7³ + 4² – 3² 351 = 7³ + 2³
352 = 7³ + 3² 353 = 17² + 8² 354 = 19² – 5² + 3²
355 = 20² – 3² – 6² 356 = 7³ + 3² + 2² 357 = 19² – 2²
358 = 18² + 5² + 3² 359 = 7³ + 4² 360 = 18² + 6²
361 = 19² 362 = 17² + 8² + 3² 363 = 7³ + 4² + 2²
364 = 20² – 6² 365 = 19² + 2² 366 = 20² – 3² – 5²
367 = 7³ + 6² – 3² 368 = 7³ + 5² 369 = 19² + 3²
370 = 17² + 9² 371 = 20² – 5² – 2² 372 = 18² + 8² – 4²
373 = 18² + 7² 374 = 19² + 2² + 3² 375 = 20² – 5²
376 = 7³ + 6² 377 = 19² + 4² 378 = 19² + 3² + 3²
379 = 20² – 5² + 2² 380 = 17² + 10² – 3² 381 = 19² + 4² + 2²
382 = 20² – 3² – 3² 383 = 20² – 3² – 2³ 384 = 20² – 4²
385 = 7³ + 6² + 3² 386 = 19² + 5² 387 = 20² – 3² – 2²
388 = 18² + 8² 389 = 17² + 10² 390 = 19² + 5² + 2²
391 = 20² – 3² 392 = 7³ + 7² 393 = 20² – 4² + 3²
394 = 7³ + 4² + 4² 395 = 20² – 3² + 2² 396 = 20² – 2²
397 = 19² + 6² 398 = 17² + 10² + 3² 399 = 7³ – 5² + 9²
400 = 20² 401 = 402 =
403 = 404 = 405 =
406 = 407 = 408 =
409 = 410 = 411 =
412 = 413 = 414 =
415 = 416 = 417 =
418 = 419 = 420 =
421 = 422 = 423 =
424 = 425 = 426 =
427 = 428 = 431 =
430 = 431 = 434 =
433 = 434 = 437 =
436 = 437 = 440 =
439 = 440 = 443 =
442 = 443 = 446 =
445 = 446 = 449 =
448 = 449 = 452 =
451 = 452 = 455 =
454 = 455 = 458 =
457 = 458 = 461 =
460 = 461 = 464 =
463 = 464 = 467 =
466 = 467 = 470 =
469 = 470 = 473 =
472 = 473 = 476 =
475 = 476 = 479 =
478 = 479 = 482 =
481 = 482 = 485 =
484 = 485 = 488 =
487 = 488 = 491 =
490 = 491 = 494 =
493 = 494 = 495 =
496 = 497 = 498 =
499 = 500 = 501 =
502 = 503 = 504 =
505 = 506 = 507 =
508 = 509 = 510 =
511 = 512 = 513 =
514 = 515 = 516 =
517 = 518 = 519 =
520 = 521 = 522 =
523 = 524 = 525 =
526 = 527 = 528 =
529 = 530 = 531 =
532 = 533 = 534 =
535 = 536 = 537 =
538 = 539 = 540 =
541 = 542 = 543 =
544 = 545 = 546 =
547 = 548 = 549 =
550 = 551 = 552 =
553 = 554 = 555 =
556 = 557 = 558 =
559 = 560 = 561 =
562 = 563 = 564 =
565 = 566 = 567 =
568 = 569 = 570 =
571 = 572 = 573 =
574 = 575 = 576 =
577 = 578 = 579 =
580 = 581 = 582 =
583 = 584 = 585 =
586 = 587 = 588 =
589 = 590 = 591 =
592 = 593 = 594 =
595 = 596 = 597 =
598 = 599 = 600 =
601 = 602 = 603 =
604 = 605 = 606 =
607 = 608 = 609 =
610 = 611 = 612 =
613 = 614 = 615 =
616 = 617 = 618 =
619 = 620 = 621 =
622 = 623 = 624 =
625 = 626 = 627 =
628 = 629 = 630 =
631 = 632 = 633 =
634 = 635 = 636 =
637 = 638 = 639 =
640 = 641 = 642 =
643 = 644 = 645 =
646 = 647 = 648 =
649 = 650 = 651 =
652 = 653 = 654 =
655 = 656 = 657 =
658 = 659 = 660 =
661 = 662 = 663 =
664 = 665 = 666 =
667 = 668 = 669 =
670 = 671 = 672 =
673 = 674 = 675 =
676 = 677 = 678 =
679 = 680 = 681 =
682 = 683 = 684 =
685 = 686 = 687 =
688 = 689 = 690 =
691 = 692 = 693 =
694 = 695 = 696 =
697 = 698 = 699 =
700 = 701 = 702 =
703 = 704 = 705 =
706 = 707 = 708 =
709 = 710 = 711 =
712 = 713 = 714 =
715 = 716 = 717 =
718 = 719 = 720 =
721 = 722 = 723 =
724 = 725 = 726 =
727 = 728 = 729 =
730 = 731 = 732 =
733 = 734 = 735 =
736 = 737 = 738 =
739 = 740 = 741 =
742 = 743 = 744 =
745 = 746 = 747 =
748 = 749 = 750 =
751 = 752 = 753 =
754 = 755 = 756 =
757 = 758 = 759 =
760 = 761 = 762 =
763 = 764 = 765 =
766 = 767 = 768 =
769 = 770 = 771 =
772 = 773 = 774 =
775 = 776 = 777 =
778 = 779 = 780 =
781 = 782 = 783 =
784 = 785 = 786 =
787 = 788 = 789 =
790 = 791 = 792 =
793 = 794 = 795 =
796 = 797 = 798 =
799 = 800 = 801 =
802 = 803 = 804 =
805 = 806 = 807 =
808 = 809 = 810 =
811 = 812 = 813 =
814 = 815 = 816 =
817 = 818 = 819 =
820 = 821 = 822 =
823 = 824 = 825 =
826 = 827 = 828 =
829 = 830 = 831 =
832 = 833 = 834 =
835 = 836 = 837 =
838 = 839 = 840 =
841 = 842 = 843 =
844 = 845 = 846 =
847 = 848 = 849 =
850 = 851 = 852 =
853 = 854 = 855 =
856 = 857 = 858 =
859 = 860 = 861 =
862 = 863 = 864 =
865 = 866 = 867 =
868 = 869 = 870 =
871 = 872 = 873 =
874 = 875 = 876 =
877 = 878 = 879 =
880 = 881 = 882 =
883 = 884 = 885 =
886 = 887 = 888 =
889 = 890 = 891 =
892 = 893 = 894 =
895 = 896 = 897 =
898 = 899 = 900 =
901 = 902 = 903 =
904 = 905 = 906 =
907 = 908 = 909 =
910 = 911 = 912 =
913 = 914 = 915 =
916 = 917 = 918 =
919 = 920 = 921 =
922 = 923 = 924 =
925 = 926 = 927 =
928 = 929 = 930 =
931 = 932 = 933 =
934 = 935 = 936 =
937 = 938 = 939 =
940 = 941 = 942 =
943 = 944 = 945 =
946 = 947 = 948 =
949 = 950 = 951 =
952 = 953 = 954 =
955 = 956 = 957 =
958 = 959 = 960 =
961 = 962 = 963 =
964 = 965 = 966 =
967 = 968 = 969 =
970 = 971 = 972 =
973 = 974 = 975 =
976 = 977 = 978 =
979 = 980 = 981 =
982 = 983 = 984 =
985 = 986 = 987 =
988 = 989 = 990 =
991 = 992 = 993 =
994 = 995 = 996 =
997 = 998 = 999 =

Special thanks to WaiKit for some checking.

Last update: 7 February 2008

2 responses

29 04 2009
teqplayer

was wiki-ing and came across http://en.wikipedia.org/wiki/Table_of_prime_factors when i was reading up on number theory. not exactly what u’re doing here, but related. also, i noted your only identifiable rule here is that all numbers must be represented by a set of arithmetic operation of powered factors, of which the minimal power is 2. well, further interesting reading: http://en.wikipedia.org/wiki/Divisibility_rule and http://en.wikipedia.org/wiki/Table_of_divisors

29 04 2009
jh

i doing w/o calculators. so bound to have errors. and they are sums/subtractions of powers of sth (integers only).

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