Let y(n) represent sum of digits of n
3.
For 10<n<999 list all the triplets (n,n+1,n+2) such that y(n),y(n+1),y(n+2)
are three successive integers
a.in any order
b.corresponding to n,n+1,n+2.
(In reply to
part a by Charlie)
If we comment out the sort, we require the order to be the same as the corresponding n's:
Now there are only 38:
14 15 16 | n n+1 n+2
17 18 19 | sod's of cubes
2744 3375 4096 | cubes
23 24 25
17 18 19
12167 13824 15625
41 42 43
26 27 28
68921 74088 79507
71 72 73
26 27 28
357911 373248 389017
77 78 79
26 27 28
456533 474552 493039
86 87 88
26 27 28
636056 658503 681472
161 162 163
26 27 28
4173281 4251528 4330747
224 225 226
26 27 28
11239424 11390625 11543176
242 243 244
35 36 37
14172488 14348907 14526784
254 255 256
35 36 37
16387064 16581375 16777216
272 273 274
26 27 28
20123648 20346417 20570824
296 297 298
35 36 37
25934336 26198073 26463592
302 303 304
35 36 37
27543608 27818127 28094464
305 306 307
35 36 37
28372625 28652616 28934443
314 315 316
35 36 37
30959144 31255875 31554496
350 351 352
26 27 28
42875000 43243551 43614208
425 426 427
44 45 46
76765625 77308776 77854483
431 432 433
35 36 37
80062991 80621568 81182737
437 438 439
35 36 37
83453453 84027672 84604519
455 456 457
44 45 46
94196375 94818816 95443993
473 474 475
35 36 37
105823817 106496424 107171875
497 498 499
35 36 37
122763473 123505992 124251499
596 597 598
35 36 37
211708736 212776173 213847192
602 603 604
35 36 37
218167208 219256227 220348864
611 612 613
35 36 37
228099131 229220928 230346397
635 636 637
44 45 46
256047875 257259456 258474853
665 666 667
44 45 46
294079625 295408296 296740963
677 678 679
35 36 37
310288733 311665752 313046839
713 714 715
44 45 46
362467097 363994344 365525875
764 765 766
44 45 46
445943744 447697125 449455096
836 837 838
44 45 46
584277056 586376253 588480472
851 852 853
35 36 37
616295051 618470208 620650477
872 873 874
44 45 46
663054848 665338617 667627624
881 882 883
53 54 55
683797841 686128968 688465387
896 897 898
35 36 37
719323136 721734273 724150792
947 948 949
44 45 46
849278123 851971392 854670349
950 951 952
35 36 37
857375000 860085351 862801408
962 963 964
44 45 46
890277128 893056347 895841344
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Posted by Charlie
on 2020-10-04 12:02:58 |
part b
