login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A090054 Numbers n which divide the number formed when their digits are sorted in descending order excluding trivial cases. 0
1750842, 15922035, 17508420, 19750842 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Trivial cases are identified as those values of n where the digits are already in descending order, like 3210 or 8222, such that DSort(n)=n. In such cases DSort(n)/n is equivalent to n/n (as in 3210/3210).
a(1) and a(2) are primitive. Clearly if DSort(n) mod n = 0, then dsort(n x 10) mod (n x 10) = 0. Therefore since 1750842 is a member, so will be 17508420, 175084200, 1750842000 and so on. The nonprimitive member 19750842 sets up the implication that 1(9...)750842 is a member. A quick test of 199750842, 1999750842 and 19999750842 seems to confirm this.
LINKS
EXAMPLE
a(1)=1750842 because the digits of 1750842 in descending order are 8754210 which is divisible by 1750842. a(24)=3105 because the digits of 3105 in ascending order are 135 and 3105 is divisible by 135.
MATHEMATICA
sdoQ[n_] := Module[{rs = FromDigits[ReverseSort[ IntegerDigits[n]]]},
rs != n && Divisible[rs, n]]; Select[Range[198*10^5], sdoQ] (* Harvey P. Dale, Sep 15 2021 *)
CROSSREFS
Sequence in context: A124068 A244073 A237307 * A186823 A095391 A234456
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 21 01:14 EDT 2024. Contains 374462 sequences. (Running on oeis4.)