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Search: id:A090053
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| A090053 |
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Numbers n divisible by the number formed when their digits are sorted in ascending order excluding trivial cases. |
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+0
3
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| 105, 108, 405, 510, 540, 702, 703, 810, 1001, 1005, 1008, 1020, 1050, 1080, 2002, 2016, 2025, 2040, 2050, 2100, 3003, 3042, 3060, 3105, 3510, 4004, 4005, 4050, 4080, 4200, 5005, 5010, 5040, 5049, 5100, 5130, 5200, 5400, 6006, 6084
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Trivial cases are identified as (1) values of n where the digits are already in ascending order, like 123 or 2228, such that ASort(n)=n, or (2) values of n where n mod 10=0 and all digits other than trailing zeros are in ascending order, like 12000 or 333500, such that ASort(n)=n/10^z, where z = the number of trailing zeros of n. In case (1) n/ASort(n) is equivalent to n/n (as in 123/123). In case (2) n/ASort(n) is 10^z (as in 12000/12). Neither of these cases is very interesting.
Sequence A084687 is a subset of this sequence, but that sequence excludes any value of n with 1 or more zero digits.
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LINKS
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C. Seggelin, Numbers Divisible by Digit Permutations.
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EXAMPLE
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a(1)=105 because the digits of 105 in ascending order are 015 and 105 is divisible by 15. a(24)=3105 because the digits of 3105 in ascending order are 135 and 3105 is divisible by 135.
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CROSSREFS
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Cf. A084687, A090055, A090056.
Sequence in context: A112814 A058179 A090055 this_sequence A096093 A039553 A135999
Adjacent sequences: A090050 A090051 A090052 this_sequence A090054 A090055 A090056
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003
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