In mathematics a polydivisible number is a number with digits abcde... that has the following properties :
- Its first digit a is not 0.
- The number formed by its first two digits ab is a multiple of 2.
- The number formed by its first three digits abc is a multiple of 3.
- The number formed by its first four digits abcd is a multiple of 4.
- etc.
For example, 345654 is a six-digit polydivisible number, but 123456 is not, because 1234 is not a multiple of 4. Polydivisible numbers can be defined in any base - however, the numbers in this article are all in base 10, so permitted digits are 0 to 9.
The smallest base 10 polydivisible numbers with 1,2,3,4... etc. digits are
1, 10, 102, 1020, 10200, 102000, 1020005, 10200056, 102000564, 1020005640 (sequence A078282 in OEIS)
Read more about Polydivisible Number: Background, How Many Polydivisible Numbers Are There?, Counting Polydivisible Numbers, Related Problems
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