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A343925
Irregular triangle read by rows: n-th row gives the numbers > 1 that can be multiplied by n the maximum number of times, see A343924, such that each product has distinct digits.
2
2, 2, 2, 2, 2, 2, 5, 2, 3, 2, 13, 14, 15, 18, 35, 72, 77, 2, 2, 5, 2, 2, 2, 3, 6, 17, 3, 13, 2, 2, 7, 12, 2, 2, 5, 39, 3, 2, 7, 17, 78, 3, 2, 2, 4, 2, 5, 9, 12, 18, 93, 3, 17, 5, 3, 2, 4, 2, 5, 2, 2, 2, 9, 2, 3, 5, 6, 7, 11, 12, 15, 21, 24, 25, 34, 59, 74, 87, 107, 113, 118, 127, 158, 173, 207
OFFSET
1,1
COMMENTS
See A343924 for the maximum number of times the numbers in each row can multiply n to produce a series of products with distinct digits.
The number of terms in each row is extremely variable. For n below 1000 the numbers 556, 748, 813, 818, 848 can only be multiplied one time before a product with non-distinct digits is produced. For 556, for example, there are 7002 different numbers which satisfy this condition, the list starting with 5, 7, 15, 17, 19, ... . In comparison the next row for 557 has one term, 25, which can be multiplied by 557 the maximum of three times.
All rows correspond to numbers ending in two or more zeros, for example 100, have no terms as any product will also end in at least that many zeros.
FORMULA
row(n) has no terms for n > 4938271605 or for any number n ending in two or more 0's.
EXAMPLE
row(1) = 2 as 1 can be multiplied by 2 the maximum of 15 times producing products with distinct digits. The products are: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16348, 32768.
row(11) = 13, 14, 15, 18, 35, 72, 77 as these numbers can be multiplied by 11 the maximum of 3 times producing products with distinct digits. For example choosing 13 the products are 143, 1859, 24167.
The table begins:
.
2;
2;
2;
2;
2;
2;
5;
2;
3;
2;
13, 14, 15, 18, 35, 72, 77;
2;
2;
5;
2;
2;
2, 3, 6, 17;
3, 13;
...
CROSSREFS
Cf. A343924, A343921 (addition), A010784, A003991, A043537.
Sequence in context: A008767 A244461 A366811 * A105255 A351023 A140818
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, May 04 2021
STATUS
approved