no new best yet, but if you're interested in doing the coding bit I did some mathy stuff
it's been a year since I last looked at this, so I decided to give it another look.
last time, we found that we have two 'numbers' that we're converting between, a 'compressed' number which is written in bijective base 250 using most of the jelly code page, and an 'uncompressed' number written in base 1/288 using digit/3
rd printable ascii. using this information, I made some code that only looks at numbers which have digits in the ascii range in base 250 and digits divisible by three in base 1/288, and was able to compare all numbers with 9 or fewer digits.
however, this is not the only information that we can use. I called it 'basically random', but there is still enough information tied up in the fact that must both have the same value and representation that we can make things more efficient. as an example, let's look at a comparison between base 12 and base 1/16. last time, I only skipped invalid numbers, which is basically like looking through this block:
b12 b1/16 value
194 001 256
195 101 257
196 201 258
197 301 259
198 401 260
199 501 261
19a 601 262
19b 701 263
1a0 801 264
1a1 901 265
1a2 a01 266
1a3 b01 267
1a4 c01 268
1a5 d01 269
1a6 e01 270
1a7 f01 271
1a8 011 272
1a9 111 273
1aa 211 274
1ab 311 275
1b0 411 276
1b1 511 277
1b2 611 278
1b3 711 279
1b4 811 280
1b5 911 281
1b6 a11 282
1b7 b11 283
1b8 c11 284
1b9 d11 285
1ba e11 286
1bb f11 287
200 021 288
201 121 289
202 221 290
203 321 291
204 421 292
205 521 293
206 621 294
207 721 295
208 821 296
209 921 297
20a a21 298
20b b21 299
210 c21 300
211 d21 301
212 e21 302
213 f21 303
214 031 304
215 131 305
216 231 306
217 331 307
218 431 308
219 531 309
21a 631 310
21b 731 311
220 831 312
221 931 313
222 a31 314
223 b31 315
224 c31 316
225 d31 317
226 e31 318
227 f31 319
228 041 320
229 141 321
22a 241 322
22b 341 323
230 441 324
231 541 325
232 641 326
233 741 327
234 841 328
235 941 329
236 a41 330
237 b41 331
238 c41 332
239 d41 333
23a e41 334
23b f41 335
240 051 336
241 151 337
242 251 338
243 351 339
244 451 340
245 551 341
246 651 342
247 751 343
248 851 344
249 951 345
24a a51 346
24b b51 347
250 c51 348
251 d51 349
252 e51 350
253 f51 351
254 061 352
255 161 353
256 261 354
257 361 355
258 461 356
259 561 357
25a 661 358
25b 761 359
260 861 360
261 961 361
262 a61 362
263 b61 363
264 c61 364
265 d61 365
266 e61 366
267 f61 367
268 071 368
269 171 369
26a 271 370
26b 371 371
270 471 372
271 571 373
272 671 374
273 771 375
274 871 376
275 971 377
276 a71 378
277 b71 379
278 c71 380
279 d71 381
27a e71 382
27b f71 383
280 081 384
281 181 385
282 281 386
283 381 387
284 481 388
285 581 389
286 681 390
287 781 391
288 881 392
289 981 393
28a a81 394
28b b81 395
290 c81 396
291 d81 397
292 e81 398
293 f81 399
294 091 400
295 191 401
296 291 402
297 391 403
298 491 404
299 591 405
29a 691 406
29b 791 407
2a0 891 408
2a1 991 409
2a2 a91 410
2a3 b91 411
2a4 c91 412
2a5 d91 413
2a6 e91 414
2a7 f91 415
2a8 0a1 416
2a9 1a1 417
2aa 2a1 418
2ab 3a1 419
2b0 4a1 420
2b1 5a1 421
2b2 6a1 422
2b3 7a1 423
2b4 8a1 424
2b5 9a1 425
2b6 aa1 426
2b7 ba1 427
2b8 ca1 428
2b9 da1 429
2ba ea1 430
2bb fa1 431
300 0b1 432
301 1b1 433
302 2b1 434
303 3b1 435
304 4b1 436
305 5b1 437
306 6b1 438
307 7b1 439
308 8b1 440
309 9b1 441
30a ab1 442
30b bb1 443
310 cb1 444
311 db1 445
312 eb1 446
313 fb1 447
314 0c1 448
315 1c1 449
316 2c1 450
317 3c1 451
318 4c1 452
319 5c1 453
31a 6c1 454
31b 7c1 455
320 8c1 456
321 9c1 457
322 ac1 458
323 bc1 459
324 cc1 460
325 dc1 461
326 ec1 462
327 fc1 463
328 0d1 464
329 1d1 465
32a 2d1 466
32b 3d1 467
330 4d1 468
331 5d1 469
332 6d1 470
333 7d1 471
334 8d1 472
335 9d1 473
336 ad1 474
337 bd1 475
338 cd1 476
339 dd1 477
33a ed1 478
33b fd1 479
340 0e1 480
341 1e1 481
342 2e1 482
343 3e1 483
344 4e1 484
345 5e1 485
346 6e1 486
347 7e1 487
348 8e1 488
349 9e1 489
34a ae1 490
34b be1 491
350 ce1 492
351 de1 493
352 ee1 494
353 fe1 495
354 0f1 496
355 1f1 497
356 2f1 498
357 3f1 499
358 4f1 500
359 5f1 501
35a 6f1 502
35b 7f1 503
360 8f1 504
361 9f1 505
362 af1 506
363 bf1 507
364 cf1 508
365 df1 509
366 ef1 510
367 ff1 511
368 002 512
369 102 513
36a 202 514
36b 302 515
370 402 516
371 502 517
372 602 518
373 702 519
374 802 520
375 902 521
376 a02 522
377 b02 523
378 c02 524
379 d02 525
37a e02 526
37b f02 527
380 012 528
381 112 529
382 212 530
383 312 531
384 412 532
385 512 533
386 612 534
387 712 535
388 812 536
389 912 537
38a a12 538
38b b12 539
390 c12 540
391 d12 541
392 e12 542
393 f12 543
394 022 544
395 122 545
396 222 546
397 322 547
398 422 548
399 522 549
39a 622 550
39b 722 551
3a0 822 552
3a1 922 553
3a2 a22 554
3a3 b22 555
3a4 c22 556
3a5 d22 557
3a6 e22 558
3a7 f22 559
3a8 032 560
3a9 132 561
3aa 232 562
3ab 332 563
3b0 432 564
3b1 532 565
3b2 632 566
3b3 732 567
3b4 832 568
3b5 932 569
3b6 a32 570
3b7 b32 571
3b8 c32 572
3b9 d32 573
3ba e32 574
3bb f32 575
400 042 576
401 142 577
402 242 578
403 342 579
404 442 580
405 542 581
406 642 582
407 742 583
408 842 584
409 942 585
40a a42 586
40b b42 587
410 c42 588
411 d42 589
412 e42 590
413 f42 591
414 052 592
415 152 593
416 252 594
417 352 595
418 452 596
419 552 597
41a 652 598
41b 752 599
420 852 600
421 952 601
422 a52 602
423 b52 603
424 c52 604
425 d52 605
426 e52 606
427 f52 607
428 062 608
429 162 609
42a 262 610
42b 362 611
430 462 612
431 562 613
432 662 614
433 762 615
434 862 616
435 962 617
436 a62 618
437 b62 619
438 c62 620
439 d62 621
43a e62 622
43b f62 623
440 072 624
441 172 625
442 272 626
443 372 627
444 472 628
445 572 629
446 672 630
447 772 631
448 872 632
449 972 633
44a a72 634
44b b72 635
450 c72 636
451 d72 637
452 e72 638
453 f72 639
454 082 640
455 182 641
456 282 642
457 382 643
458 482 644
459 582 645
45a 682 646
45b 782 647
460 882 648
461 982 649
462 a82 650
463 b82 651
464 c82 652
465 d82 653
466 e82 654
467 f82 655
468 092 656
469 192 657
46a 292 658
46b 392 659
470 492 660
471 592 661
472 692 662
473 792 663
474 892 664
475 992 665
476 a92 666
477 b92 667
478 c92 668
479 d92 669
47a e92 670
47b f92 671
480 0a2 672
481 1a2 673
482 2a2 674
483 3a2 675
484 4a2 676
485 5a2 677
486 6a2 678
487 7a2 679
488 8a2 680
489 9a2 681
48a aa2 682
48b ba2 683
490 ca2 684
491 da2 685
492 ea2 686
493 fa2 687
494 0b2 688
495 1b2 689
496 2b2 690
497 3b2 691
498 4b2 692
499 5b2 693
49a 6b2 694
49b 7b2 695
4a0 8b2 696
4a1 9b2 697
4a2 ab2 698
4a3 bb2 699
4a4 cb2 700
4a5 db2 701
4a6 eb2 702
4a7 fb2 703
4a8 0c2 704
4a9 1c2 705
4aa 2c2 706
4ab 3c2 707
4b0 4c2 708
4b1 5c2 709
4b2 6c2 710
4b3 7c2 711
4b4 8c2 712
4b5 9c2 713
4b6 ac2 714
4b7 bc2 715
4b8 cc2 716
4b9 dc2 717
4ba ec2 718
4bb fc2 719
500 0d2 720
501 1d2 721
502 2d2 722
503 3d2 723
504 4d2 724
505 5d2 725
506 6d2 726
507 7d2 727
508 8d2 728
509 9d2 729
50a ad2 730
50b bd2 731
510 cd2 732
511 dd2 733
512 ed2 734
513 fd2 735
514 0e2 736
515 1e2 737
516 2e2 738
517 3e2 739
518 4e2 740
519 5e2 741
51a 6e2 742
51b 7e2 743
520 8e2 744
521 9e2 745
522 ae2 746
523 be2 747
524 ce2 748
525 de2 749
526 ee2 750
527 fe2 751
528 0f2 752
529 1f2 753
52a 2f2 754
52b 3f2 755
530 4f2 756
531 5f2 757
532 6f2 758
533 7f2 759
534 8f2 760
535 9f2 761
536 af2 762
537 bf2 763
538 cf2 764
539 df2 765
53a ef2 766
53b ff2 767
540 003 768
541 103 769
542 203 770
543 303 771
544 403 772
545 503 773
546 603 774
547 703 775
548 803 776
549 903 777
54a a03 778
54b b03 779
550 c03 780
551 d03 781
552 e03 782
553 f03 783
554 013 784
555 113 785
556 213 786
557 313 787
558 413 788
559 513 789
55a 613 790
55b 713 791
560 813 792
561 913 793
562 a13 794
563 b13 795
564 c13 796
565 d13 797
566 e13 798
567 f13 799
568 023 800
569 123 801
56a 223 802
56b 323 803
570 423 804
571 523 805
572 623 806
573 723 807
574 823 808
575 923 809
576 a23 810
577 b23 811
578 c23 812
579 d23 813
57a e23 814
57b f23 815
580 033 816
581 133 817
582 233 818
583 333 819
584 433 820
585 533 821
586 633 822
587 733 823
588 833 824
589 933 825
58a a33 826
58b b33 827
590 c33 828
591 d33 829
592 e33 830
593 f33 831
594 043 832
595 143 833
596 243 834
597 343 835
598 443 836
599 543 837
59a 643 838
59b 743 839
5a0 843 840
5a1 943 841
5a2 a43 842
5a3 b43 843
5a4 c43 844
5a5 d43 845
5a6 e43 846
5a7 f43 847
5a8 053 848
5a9 153 849
5aa 253 850
5ab 353 851
5b0 453 852
5b1 553 853
5b2 653 854
5b3 753 855
5b4 853 856
5b5 953 857
5b6 a53 858
5b7 b53 859
5b8 c53 860
5b9 d53 861
5ba e53 862
5bb f53 863
600 063 864
601 163 865
602 263 866
603 363 867
604 463 868
605 563 869
606 663 870
607 763 871
608 863 872
609 963 873
60a a63 874
60b b63 875
610 c63 876
611 d63 877
612 e63 878
613 f63 879
614 073 880
615 173 881
616 273 882
617 373 883
618 473 884
619 573 885
61a 673 886
61b 773 887
620 873 888
621 973 889
622 a73 890
623 b73 891
624 c73 892
625 d73 893
626 e73 894
627 f73 895
628 083 896
629 183 897
62a 283 898
62b 383 899
630 483 900
631 583 901
632 683 902
633 783 903
634 883 904
635 983 905
636 a83 906
637 b83 907
638 c83 908
639 d83 909
63a e83 910
63b f83 911
640 093 912
641 193 913
642 293 914
643 393 915
644 493 916
645 593 917
646 693 918
647 793 919
648 893 920
649 993 921
64a a93 922
64b b93 923
650 c93 924
651 d93 925
652 e93 926
653 f93 927
654 0a3 928
655 1a3 929
656 2a3 930
657 3a3 931
658 4a3 932
659 5a3 933
65a 6a3 934
65b 7a3 935
660 8a3 936
661 9a3 937
662 aa3 938
663 ba3 939
664 ca3 940
665 da3 941
666 ea3 942
667 fa3 943
668 0b3 944
669 1b3 945
66a 2b3 946
66b 3b3 947
670 4b3 948
671 5b3 949
672 6b3 950
673 7b3 951
674 8b3 952
675 9b3 953
676 ab3 954
677 bb3 955
678 cb3 956
679 db3 957
67a eb3 958
67b fb3 959
680 0c3 960
681 1c3 961
682 2c3 962
683 3c3 963
684 4c3 964
685 5c3 965
686 6c3 966
687 7c3 967
688 8c3 968
689 9c3 969
68a ac3 970
68b bc3 971
690 cc3 972
691 dc3 973
692 ec3 974
693 fc3 975
694 0d3 976
695 1d3 977
696 2d3 978
697 3d3 979
698 4d3 980
699 5d3 981
69a 6d3 982
69b 7d3 983
6a0 8d3 984
6a1 9d3 985
6a2 ad3 986
6a3 bd3 987
6a4 cd3 988
6a5 dd3 989
6a6 ed3 990
6a7 fd3 991
6a8 0e3 992
6a9 1e3 993
6aa 2e3 994
6ab 3e3 995
6b0 4e3 996
6b1 5e3 997
6b2 6e3 998
6b3 7e3 999
6b4 8e3 1000
6b5 9e3 1001
6b6 ae3 1002
6b7 be3 1003
6b8 ce3 1004
6b9 de3 1005
6ba ee3 1006
6bb fe3 1007
700 0f3 1008
701 1f3 1009
702 2f3 1010
703 3f3 1011
704 4f3 1012
705 5f3 1013
706 6f3 1014
707 7f3 1015
708 8f3 1016
709 9f3 1017
70a af3 1018
70b bf3 1019
710 cf3 1020
711 df3 1021
712 ef3 1022
713 ff3 1023
714 004 1024
715 104 1025
716 204 1026
717 304 1027
718 404 1028
719 504 1029
71a 604 1030
71b 704 1031
720 804 1032
721 904 1033
722 a04 1034
723 b04 1035
724 c04 1036
725 d04 1037
726 e04 1038
727 f04 1039
728 014 1040
729 114 1041
72a 214 1042
72b 314 1043
730 414 1044
731 514 1045
732 614 1046
733 714 1047
734 814 1048
735 914 1049
736 a14 1050
737 b14 1051
738 c14 1052
739 d14 1053
73a e14 1054
73b f14 1055
740 024 1056
741 124 1057
742 224 1058
743 324 1059
744 424 1060
745 524 1061
746 624 1062
747 724 1063
748 824 1064
749 924 1065
74a a24 1066
74b b24 1067
750 c24 1068
751 d24 1069
752 e24 1070
753 f24 1071
754 034 1072
755 134 1073
756 234 1074
757 334 1075
758 434 1076
759 534 1077
75a 634 1078
75b 734 1079
760 834 1080
761 934 1081
762 a34 1082
763 b34 1083
764 c34 1084
765 d34 1085
766 e34 1086
767 f34 1087
768 044 1088
769 144 1089
76a 244 1090
76b 344 1091
770 444 1092
771 544 1093
772 644 1094
773 744 1095
774 844 1096
775 944 1097
776 a44 1098
777 b44 1099
778 c44 1100
779 d44 1101
77a e44 1102
77b f44 1103
780 054 1104
781 154 1105
782 254 1106
783 354 1107
784 454 1108
785 554 1109
786 654 1110
787 754 1111
788 854 1112
789 954 1113
78a a54 1114
78b b54 1115
790 c54 1116
791 d54 1117
792 e54 1118
793 f54 1119
794 064 1120
795 164 1121
796 264 1122
797 364 1123
798 464 1124
799 564 1125
79a 664 1126
79b 764 1127
7a0 864 1128
7a1 964 1129
7a2 a64 1130
7a3 b64 1131
7a4 c64 1132
7a5 d64 1133
7a6 e64 1134
7a7 f64 1135
7a8 074 1136
7a9 174 1137
7aa 274 1138
7ab 374 1139
7b0 474 1140
7b1 574 1141
7b2 674 1142
7b3 774 1143
7b4 874 1144
7b5 974 1145
7b6 a74 1146
7b7 b74 1147
7b8 c74 1148
7b9 d74 1149
7ba e74 1150
7bb f74 1151
800 084 1152
801 184 1153
802 284 1154
803 384 1155
804 484 1156
805 584 1157
806 684 1158
807 784 1159
808 884 1160
809 984 1161
80a a84 1162
80b b84 1163
810 c84 1164
811 d84 1165
812 e84 1166
813 f84 1167
814 094 1168
815 194 1169
816 294 1170
817 394 1171
818 494 1172
819 594 1173
81a 694 1174
81b 794 1175
820 894 1176
821 994 1177
822 a94 1178
823 b94 1179
824 c94 1180
825 d94 1181
826 e94 1182
827 f94 1183
828 0a4 1184
829 1a4 1185
82a 2a4 1186
82b 3a4 1187
830 4a4 1188
831 5a4 1189
832 6a4 1190
833 7a4 1191
834 8a4 1192
835 9a4 1193
836 aa4 1194
837 ba4 1195
838 ca4 1196
839 da4 1197
83a ea4 1198
83b fa4 1199
840 0b4 1200
841 1b4 1201
842 2b4 1202
843 3b4 1203
844 4b4 1204
845 5b4 1205
846 6b4 1206
847 7b4 1207
848 8b4 1208
849 9b4 1209
84a ab4 1210
84b bb4 1211
850 cb4 1212
851 db4 1213
852 eb4 1214
853 fb4 1215
854 0c4 1216
855 1c4 1217
856 2c4 1218
857 3c4 1219
858 4c4 1220
859 5c4 1221
85a 6c4 1222
85b 7c4 1223
860 8c4 1224
861 9c4 1225
862 ac4 1226
863 bc4 1227
864 cc4 1228
865 dc4 1229
866 ec4 1230
867 fc4 1231
868 0d4 1232
869 1d4 1233
86a 2d4 1234
86b 3d4 1235
870 4d4 1236
871 5d4 1237
872 6d4 1238
873 7d4 1239
874 8d4 1240
875 9d4 1241
876 ad4 1242
877 bd4 1243
878 cd4 1244
879 dd4 1245
87a ed4 1246
87b fd4 1247
880 0e4 1248
881 1e4 1249
882 2e4 1250
883 3e4 1251
884 4e4 1252
885 5e4 1253
886 6e4 1254
887 7e4 1255
888 8e4 1256
889 9e4 1257
88a ae4 1258
88b be4 1259
890 ce4 1260
891 de4 1261
892 ee4 1262
893 fe4 1263
894 0f4 1264
895 1f4 1265
896 2f4 1266
897 3f4 1267
898 4f4 1268
899 5f4 1269
89a 6f4 1270
89b 7f4 1271
8a0 8f4 1272
8a1 9f4 1273
8a2 af4 1274
8a3 bf4 1275
8a4 cf4 1276
8a5 df4 1277
8a6 ef4 1278
8a7 ff4 1279
8a8 005 1280
8a9 105 1281
8aa 205 1282
8ab 305 1283
8b0 405 1284
8b1 505 1285
8b2 605 1286
8b3 705 1287
8b4 805 1288
8b5 905 1289
8b6 a05 1290
8b7 b05 1291
8b8 c05 1292
8b9 d05 1293
8ba e05 1294
8bb f05 1295
900 015 1296
901 115 1297
902 215 1298
903 315 1299
904 415 1300
905 515 1301
906 615 1302
907 715 1303
908 815 1304
909 915 1305
90a a15 1306
90b b15 1307
910 c15 1308
911 d15 1309
912 e15 1310
913 f15 1311
914 025 1312
915 125 1313
916 225 1314
917 325 1315
918 425 1316
919 525 1317
91a 625 1318
91b 725 1319
920 825 1320
921 925 1321
922 a25 1322
923 b25 1323
924 c25 1324
925 d25 1325
926 e25 1326
927 f25 1327
928 035 1328
929 135 1329
92a 235 1330
92b 335 1331
930 435 1332
931 535 1333
932 635 1334
933 735 1335
934 835 1336
935 935 1337
936 a35 1338
937 b35 1339
938 c35 1340
939 d35 1341
93a e35 1342
93b f35 1343
940 045 1344
941 145 1345
942 245 1346
943 345 1347
944 445 1348
945 545 1349
946 645 1350
947 745 1351
948 845 1352
949 945 1353
94a a45 1354
94b b45 1355
950 c45 1356
951 d45 1357
952 e45 1358
953 f45 1359
954 055 1360
955 155 1361
956 255 1362
957 355 1363
958 455 1364
959 555 1365
95a 655 1366
95b 755 1367
960 855 1368
961 955 1369
962 a55 1370
963 b55 1371
964 c55 1372
965 d55 1373
966 e55 1374
967 f55 1375
968 065 1376
969 165 1377
96a 265 1378
96b 365 1379
970 465 1380
971 565 1381
972 665 1382
973 765 1383
974 865 1384
975 965 1385
976 a65 1386
977 b65 1387
978 c65 1388
979 d65 1389
97a e65 1390
97b f65 1391
980 075 1392
981 175 1393
982 275 1394
983 375 1395
984 475 1396
985 575 1397
986 675 1398
987 775 1399
988 875 1400
989 975 1401
98a a75 1402
98b b75 1403
990 c75 1404
991 d75 1405
992 e75 1406
993 f75 1407
994 085 1408
995 185 1409
996 285 1410
997 385 1411
998 485 1412
999 585 1413
99a 685 1414
99b 785 1415
9a0 885 1416
9a1 985 1417
9a2 a85 1418
9a3 b85 1419
9a4 c85 1420
9a5 d85 1421
9a6 e85 1422
9a7 f85 1423
9a8 095 1424
9a9 195 1425
9aa 295 1426
9ab 395 1427
9b0 495 1428
9b1 595 1429
9b2 695 1430
9b3 795 1431
9b4 895 1432
9b5 995 1433
9b6 a95 1434
9b7 b95 1435
9b8 c95 1436
9b9 d95 1437
9ba e95 1438
9bb f95 1439
a00 0a5 1440
a01 1a5 1441
a02 2a5 1442
a03 3a5 1443
a04 4a5 1444
a05 5a5 1445
a06 6a5 1446
a07 7a5 1447
a08 8a5 1448
a09 9a5 1449
a0a aa5 1450
a0b ba5 1451
a10 ca5 1452
a11 da5 1453
a12 ea5 1454
a13 fa5 1455
a14 0b5 1456
a15 1b5 1457
a16 2b5 1458
a17 3b5 1459
a18 4b5 1460
a19 5b5 1461
a1a 6b5 1462
a1b 7b5 1463
a20 8b5 1464
a21 9b5 1465
a22 ab5 1466
a23 bb5 1467
a24 cb5 1468
a25 db5 1469
a26 eb5 1470
a27 fb5 1471
a28 0c5 1472
a29 1c5 1473
a2a 2c5 1474
a2b 3c5 1475
a30 4c5 1476
a31 5c5 1477
a32 6c5 1478
a33 7c5 1479
a34 8c5 1480
a35 9c5 1481
a36 ac5 1482
a37 bc5 1483
a38 cc5 1484
a39 dc5 1485
a3a ec5 1486
a3b fc5 1487
a40 0d5 1488
a41 1d5 1489
a42 2d5 1490
a43 3d5 1491
a44 4d5 1492
a45 5d5 1493
a46 6d5 1494
a47 7d5 1495
a48 8d5 1496
a49 9d5 1497
a4a ad5 1498
a4b bd5 1499
a50 cd5 1500
a51 dd5 1501
a52 ed5 1502
a53 fd5 1503
a54 0e5 1504
a55 1e5 1505
a56 2e5 1506
a57 3e5 1507
a58 4e5 1508
a59 5e5 1509
a5a 6e5 1510
a5b 7e5 1511
a60 8e5 1512
a61 9e5 1513
a62 ae5 1514
a63 be5 1515
a64 ce5 1516
a65 de5 1517
a66 ee5 1518
a67 fe5 1519
a68 0f5 1520
a69 1f5 1521
a6a 2f5 1522
a6b 3f5 1523
a70 4f5 1524
a71 5f5 1525
a72 6f5 1526
a73 7f5 1527
a74 8f5 1528
a75 9f5 1529
a76 af5 1530
a77 bf5 1531
a78 cf5 1532
a79 df5 1533
a7a ef5 1534
a7b ff5 1535
a80 006 1536
a81 106 1537
a82 206 1538
a83 306 1539
a84 406 1540
a85 506 1541
a86 606 1542
a87 706 1543
a88 806 1544
a89 906 1545
a8a a06 1546
a8b b06 1547
a90 c06 1548
a91 d06 1549
a92 e06 1550
a93 f06 1551
a94 016 1552
a95 116 1553
a96 216 1554
a97 316 1555
a98 416 1556
a99 516 1557
a9a 616 1558
a9b 716 1559
aa0 816 1560
aa1 916 1561
aa2 a16 1562
aa3 b16 1563
aa4 c16 1564
aa5 d16 1565
aa6 e16 1566
aa7 f16 1567
aa8 026 1568
aa9 126 1569
aaa 226 1570
aab 326 1571
ab0 426 1572
ab1 526 1573
ab2 626 1574
ab3 726 1575
ab4 826 1576
ab5 926 1577
ab6 a26 1578
ab7 b26 1579
ab8 c26 1580
ab9 d26 1581
aba e26 1582
abb f26 1583
b00 036 1584
b01 136 1585
b02 236 1586
b03 336 1587
b04 436 1588
b05 536 1589
b06 636 1590
b07 736 1591
b08 836 1592
b09 936 1593
b0a a36 1594
b0b b36 1595
b10 c36 1596
b11 d36 1597
b12 e36 1598
b13 f36 1599
b14 046 1600
b15 146 1601
b16 246 1602
b17 346 1603
b18 446 1604
b19 546 1605
b1a 646 1606
b1b 746 1607
b20 846 1608
b21 946 1609
b22 a46 1610
b23 b46 1611
b24 c46 1612
b25 d46 1613
b26 e46 1614
b27 f46 1615
b28 056 1616
b29 156 1617
b2a 256 1618
b2b 356 1619
b30 456 1620
b31 556 1621
b32 656 1622
b33 756 1623
b34 856 1624
b35 956 1625
b36 a56 1626
b37 b56 1627
b38 c56 1628
b39 d56 1629
b3a e56 1630
b3b f56 1631
b40 066 1632
b41 166 1633
b42 266 1634
b43 366 1635
b44 466 1636
b45 566 1637
b46 666 1638
b47 766 1639
b48 866 1640
b49 966 1641
b4a a66 1642
b4b b66 1643
b50 c66 1644
b51 d66 1645
b52 e66 1646
b53 f66 1647
b54 076 1648
b55 176 1649
b56 276 1650
b57 376 1651
b58 476 1652
b59 576 1653
b5a 676 1654
b5b 776 1655
b60 876 1656
b61 976 1657
b62 a76 1658
b63 b76 1659
b64 c76 1660
b65 d76 1661
b66 e76 1662
b67 f76 1663
b68 086 1664
b69 186 1665
b6a 286 1666
b6b 386 1667
b70 486 1668
b71 586 1669
b72 686 1670
b73 786 1671
b74 886 1672
b75 986 1673
b76 a86 1674
b77 b86 1675
b78 c86 1676
b79 d86 1677
b7a e86 1678
b7b f86 1679
b80 096 1680
b81 196 1681
b82 296 1682
b83 396 1683
b84 496 1684
b85 596 1685
b86 696 1686
b87 796 1687
b88 896 1688
b89 996 1689
b8a a96 1690
b8b b96 1691
b90 c96 1692
b91 d96 1693
b92 e96 1694
b93 f96 1695
b94 0a6 1696
b95 1a6 1697
b96 2a6 1698
b97 3a6 1699
b98 4a6 1700
b99 5a6 1701
b9a 6a6 1702
b9b 7a6 1703
ba0 8a6 1704
ba1 9a6 1705
ba2 aa6 1706
ba3 ba6 1707
ba4 ca6 1708
ba5 da6 1709
ba6 ea6 1710
ba7 fa6 1711
ba8 0b6 1712
ba9 1b6 1713
baa 2b6 1714
bab 3b6 1715
bb0 4b6 1716
bb1 5b6 1717
bb2 6b6 1718
bb3 7b6 1719
bb4 8b6 1720
bb5 9b6 1721
bb6 ab6 1722
bb7 bb6 1723
bb8 cb6 1724
bb9 db6 1725
bba eb6 1726
bbb fb6 1727
if you spend a lot of time looking at this, you will quickly realize that there are some patterns you can use to skip a lot of numbers when you're looking for a number with the same representation. for example, if instead of incrementing the value by one, you move it up to the next time one side of the number could potentially match, you get lists looking more like this:
left match: right match:
dec b12 1/16 b12 16⁻ dec
256 194 001 194 001 256
257 195 101 1a1 901 265
273 1a9 111 1b1 511 277
289 201 121 201 121 289
290 202 221 211 d21 301
306 216 231 221 931 313
322 22a 241 231 541 325
338 242 251 241 151 337
354 256 261 251 d51 349
370 26a 271 261 961 361
386 282 281 271 571 373
402 296 291 281 181 385
418 2aa 2a1 291 d81 397
434 302 2b1 2a1 991 409
435 303 3b1 2b1 5a1 421
451 317 3c1 301 1b1 433
467 32b 3d1 311 db1 445
483 343 3e1 321 9c1 457
499 357 3f1 331 5d1 469
515 36b 302 341 1e1 481
531 383 312 351 de1 493
547 397 322 361 9f1 505
563 3ab 332 371 502 517
579 403 342 372 602 518
580 404 442 382 212 530
596 418 452 392 e12 542
612 430 462 3a2 a22 554
628 444 472 3b2 632 566
644 458 482 402 242 578
660 470 492 412 e42 590
676 484 4a2 422 a52 602
692 498 4b2 432 662 614
708 4b0 4c2 442 272 626
724 504 4d2 452 e72 638
725 505 5d2 462 a82 650
741 519 5e2 472 692 662
757 531 5f2 482 2a2 674
773 545 503 492 ea2 686
789 559 513 4a2 ab2 698
805 571 523 4b2 6c2 710
821 585 533 502 2d2 722
837 599 543 512 ed2 734
853 5b1 553 522 ae2 746
869 605 563 532 6f2 758
870 606 663 543 303 771
886 61a 673 553 f03 783
902 632 683 563 b13 795
918 646 693 573 723 807
934 65a 6a3 583 333 819
950 672 6b3 593 f33 831
966 686 6c3 5a3 b43 843
982 69a 6d3 5b3 753 855
998 6b2 6e3 603 363 867
1014 706 6f3 613 f63 879
1015 707 7f3 623 b73 891
1031 71b 704 633 783 903
1047 733 714 643 393 915
1063 747 724 653 f93 927
1079 75b 734 663 ba3 939
1095 773 744 673 7b3 951
1111 787 754 683 3c3 963
1127 79b 764 693 fc3 975
1143 7b3 774 6a3 bd3 987
1159 807 784 6b3 7e3 999
1160 808 884 703 3f3 1011
1176 820 894 713 ff3 1023
1192 834 8a4 714 004 1024
1208 848 8b4 724 c04 1036
1224 860 8c4 734 814 1048
1240 874 8d4 744 424 1060
1256 888 8e4 754 034 1072
1272 8a0 8f4 764 c34 1084
1288 8b4 805 774 844 1096
1304 908 815 784 454 1108
1305 909 915 794 064 1120
1321 921 925 7a4 c64 1132
1337 935 935 7b4 874 1144
1353 949 945 804 484 1156
1369 961 955 814 094 1168
1385 975 965 824 c94 1180
1401 989 975 834 8a4 1192
1417 9a1 985 844 4b4 1204
1433 9b5 995 854 0c4 1216
1449 a09 9a5 864 cc4 1228
1450 a0a aa5 874 8d4 1240
1466 a22 ab5 884 4e4 1252
1482 a36 ac5 894 0f4 1264
1498 a4a ad5 8a4 cf4 1276
1514 a62 ae5 8b4 805 1288
1530 a76 af5 8b5 905 1289
1546 a8a a06 905 515 1301
1562 aa2 a16 915 125 1313
1578 ab6 a26 925 d25 1325
1594 b0a a36 935 935 1337
1595 b0b b36 945 545 1349
1611 b23 b46 955 155 1361
1627 b37 b56 965 d55 1373
1643 b4b b66 975 965 1385
1659 b63 b76 985 575 1397
1675 b77 b86 995 185 1409
1691 b8b b96 9a5 d85 1421
1707 ba3 ba6 9b5 995 1433
1723 bb7 bb6 a05 5a5 1445
a15 1b5 1457
a25 db5 1469
a35 9c5 1481
a45 5d5 1493
a55 1e5 1505
a65 de5 1517
a75 9f5 1529
a85 506 1541
a86 606 1542
a96 216 1554
aa6 e16 1566
ab6 a26 1578
b06 636 1590
b16 246 1602
b26 e46 1614
b36 a56 1626
b46 666 1638
b56 276 1650
b66 e76 1662
b76 a86 1674
b86 696 1686
b96 2a6 1698
ba6 ea6 1710
bb6 ab6 1722
I'm sure someone more clever than me could find a way to combine this information to look through the intersection of these lists rather than the union, which is short enough to easily spot the answer in this example case:
201 121 289
834 8a4 1192
874 8d4 1240
8b4 805 1288
935 935 1337
975 965 1385
9b5 995 1433
ab6 a26 1578
but even the union of the two sets is much, much faster to look through than the original combinatorial product. after some test runs, is looking like I'll be able to check up to 15 digits with this; but it's not looking great. in the 8-11 range I'm only getting results with at least two digits off, and past that so far I have only gotten answers with three digits wrong. I'm still debugging my code and should have some time to finish it around new years', but until then I'll at least share the code that's mostly working:
const LEN:usize = 8; //note: raw can only be u128 up to LEN 16. for 17 or more, you'll need a bigger type.
const ERR:usize = 2;
const LEFT:bool = true;
use std::process;
type Num = [u8; LEN];
fn from250(b250: Num, curr: Num) -> (Num,bool) {
let mut raw:u128 = 0;
for i in 0..LEN {raw += b250[i] as u128 * 250u128.pow(i as u32);}
// let tmp = raw;
let mut b288:Num = [0u8; LEN];
for i in (0..LEN).rev() {
if raw % 3 == 0 {
b288[i] = (raw%288/3) as u8;
raw /= 288;
} else {
for j in i..LEN { b288[j] = 0; }
b288[i] = (raw%288/3+1) as u8;
if b288[i] == 96 { b288[i] = 0; raw += 288 /* *3? */ ; }
raw /= 288;
}
}
// let test: String = b288.map(|x| (x+32) as char).iter().rev().collect();
// println!("\t\t'{test}'\t{tmp}");
(b288, b288 != curr)
}
fn from288(b288: Num) -> Num {
let mut raw:u128 = 0;
for i in 0..LEN {raw += b288[i] as u128 * 3u128 * 288u128.pow((LEN-i-1) as u32);}
// let tmp = raw;
let mut b250:Num = [0u8; LEN];
for i in 0..LEN { b250[i] = (raw%250) as u8; raw /= 250; }
for i in (0..LEN).rev() {
if b250[i] < 33 {
for j in 0..=i { b250[j] = 33; }
break;
} else if b250[i] > 128 {
if i == LEN-1 {process::exit(0);}
b250[i+1] += 1;
for j in 0..=i { b250[j] = 33; }
break;
}
}
// let test: String = b250.map(|x| (x-1) as char).iter().rev().collect();
// println!("“{test}»\t\t\t{tmp}");
b250
}
fn similar(b288: Num, b250: Num) {
let mut count = 0;
for i in 0..LEN { if b250[i] == b288[i] + 33 { count += 1; } }
if count >= LEN-ERR {
const ASCII: &str = " !\"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~¶";
let mut s250: [char; LEN] = ['a'; LEN];
let mut s288: [char; LEN] = ['a'; LEN];
for i in 0..LEN { s250[i] = ASCII.chars().collect::<Vec <char>>()[b250[i] as usize - 33]; }
for i in 0..LEN { s288[i] = ASCII.chars().collect::<Vec <char>>()[b288[i] as usize]; }
let s250: String = s250.iter().rev().collect();
let s288: String = s288.iter().rev().collect();
let mut raw = 0u128;
for i in 0..LEN {raw += b288[i] as u128 * 3 * 288u128.pow((LEN-i-1).try_into().unwrap()); }
println!("“{s250}»\t'{s288}'\t{raw}\t{count}");
}
}
fn main() {
let mut bool = true;
let mut b288 = [0u8; LEN];
let mut b250 = [0u8; LEN];
while b288[0] <= 95 {
while bool { // finds the next valid pair of numbers
b250 = from288(b288);
(b288,bool) = from250(b250,b288);
}
similar(b288, b250);
if LEFT { // pseudocode for fining next number
//if left(b288) == left(b250) { center(b288) += 1; }
//else if left(b288) < left(b250) { left(b288) = left(b250); }
//else { more logic needs to be done here, but the first two should take care of most cases. digit rollover and the fact that we're skipping invalid numbers might come into play here. }
} else { // the same thing but mirrored; right(b250) gets increased to right(288)
} // note that for even LENs, neither 'center' number is part of the left or right.
bool = true;
//incrementing by one:
//b288[LEN] += 1;
} // see also https://tio.run/##y0rNyan8//9Rw5ykQ7v///8PAA
}// and https://tio.run/##ARoA5f9qZWxsef//4biDw5jigbXhu4vDmEr///85OQ
// for checking answers. raw goes into the 'arguments' of the second link,
// and the output of that goes into the quotes in the first link
```