Let N
0=348364879.
The digital product of N, that is, the product of its nonzero digits, is P0=3483648, which is contained within N0.
Find additional examples of numbers that contain their own digital products, with N0<N1<N2<N3... and P0<P1<P2<P3...
(In reply to
method of solution by Charlie)
To make an example, rearrange any line's "digits" with as many interspersed 1's as needed, so that the "product" from the left hand column is formed. After that, as many 1's can be added where necessary, without disturbing the embedded copy of the product, to make the arithmetic order of the N values match the arithmetic order of the products.
product digits
1
9 9
8 8
7 7
6 6
18816 67788
5 5
175 557
1575 5579
4 4
1176 4677
11664 46699
144 449
6144 44688
3 3
15 35
135 359
735 3577
13716864 346677899
384 3448
1344 34447
315 3357
1575 33557
139968 3346899
11664 334669
144 3344
3483648 334467889
1316818944 334466778899
135 3335
13395375 3335557799
13716864 3334667789
2 2
128 288
112 278
12 26
6912 26889
672 2678
186624 2466899
16128 246678
14112 246677
14112 244779
124416 2446899
82944 2446689
27869184 2446667889
82944 2444899
6912 244469
6144 244468
27869184 2444678899
36 236
2916 23699
16128 236788
216 2366
139968 2366899
24 234
13824 234889
1296 23469
188116992 23466678899
1741824 234466789
1741824 234447899
18432 2344468
124416 23444669
93312 2338899
432 23346
34992 2334699
186624 23346689
13436928 2334668899
163296 23346679
18432 2334488
14112 2334477
13824 2334468
124416 23344689
438939648 233446778899
93312 23344669
93312 23344499
82944 23344489
442368 233444688
3981312 2334446889
27869184 23344467889
146313216 233444667789
161243136 233444666899
2916 233369
13824 2333488
93312 23334689
146313216 233346667788
188116992 233344678899
1316818944 2333446778899
161243136 233344668899
1741824 2333446678
13436928 23334466689
1741824 2333444789
13436928 23334446899
124416 233344466
376233984 2333444666789
216 2269
1176 22677
1296 22669
128 2248
112 2247
6912 224689
672 22467
221184 22466688
12192768 2246667789
221184 22446889
24192 2244679
1741824 224467899
12192768 2244677899
124416 22446669
9289728 2244478899
124416 22444699
4128768 2244466788
12 223
27216 2236679
12192768 2236677889
163296 22366679
432 22349
384 22348
248832 22348899
24192 2234789
18432 2234688
16128 2234678
14112 2234677
13824 2234668
13824 2234489
12288 2234488
1344 223447
82944 22344689
442368 223446688
27869184 22344667889
219469824 223446677899
2612736 2234466679
221184 223444668
23328 2233899
216 22336
139968 22336899
93312 22336689
93312 22334899
42336 22334677
3429216 2233467799
27433728 22334677899
2612736 2233466789
188116992 223346678899
146313216 223346677889
161243136 223346668899
221184 223344688
1741824 2233446789
12192768 22334467789
13436928 22334466899
124416 223344666
18432 22334448
124416 223344469
126414618624 2233444666778899
2939328 2233367899
27216 22333667
13226976 22333666799
432 223334
34992 22333499
248832 223334889
2239488 2233348899
13436928 22333468899
376233984 2233346667889
13824 22333448
93312 223334469
376233984 2233344678899
2612736 22333446667
146313216 2233344666778
3981312 22333444889
161243136 2233344466899
27216 2226799
12192768 2226778899
16128 2226678
224 22247
14112 2224779
12288 2224688
27869184 22246667889
82944 22244899
6912 2224469
6144 2224468
27869184 22244678899
221184 222446668
221184 222444689
1296 222369
2612736 2223666789
188116992 222366678899
221184 222346688
12192768 22234667789
221184 222344889
24192 22234479
1741824 2223447899
18432 22234468
124416 222344669
4128768 22234446788
442368 2223444668
84276412416 2223444666778899
27216 22233679
12192768 22233677889
163296 222336679
18432 22233488
14112 22233477
13824 22233468
93312 222334669
93312 222334499
82944 222334489
442368 2223344688
3981312 22233446889
27869184 222334467889
219469824 2223344677899
2612736 22233446679
146313216 2223344667789
161243136 2223344666899
221184 2223344468
36118462464 2223344466678899
93312 222333689
2612736 22233366678
27433728 222333477899
188116992 2223334678899
161243136 2223334668899
13436928 222333466689
221184 2223334488
1741824 22233344789
13436928 222333446899
124416 2223334466
376233984 22233344666789
376233984 22233344467899
146313216 22233344466677
84276412416 22233344466677889
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Posted by Charlie
on 2023-11-25 14:03:01 |
list of available digit sets
