OFFSET
1,1
COMMENTS
Trivial permutations are identified as those where the permutation = k itself. Digit loss occurs when a permutation has 0 in the most significant position, which drops off, leaving a number with fewer digits. For example, when k is 3105, the permutation 0315 is excluded because 315 has fewer digits than 3105. These exclusions make this sequence a subsequence of A090055. A084687 is a subsequence of this sequence.
Apparently each term of this sequence is divisible by 3. This has been confirmed for the first 100 terms.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..362
C. Seggelin, Numbers Divisible by Digit Permutations.
EXAMPLE
a(1)=3105 because 3105 is divisible by 1035, a nontrivial permutation of 3105 with the same number of digits.
a(4)=8316 because 8316 is divisible by 1386, a nontrivial permutation of 8316 with the same number of digits.
MATHEMATICA
dnpQ[n_]:=Module[{d=FromDigits/@Select[Permutations[IntegerDigits[n]], First[#]>0&&Reverse[#]!=#&]}, Count[Divisible[n, d], True]>1]; Select[ Range[90000], dnpQ] (* Harvey P. Dale, Aug 19 2013 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 21 2003
STATUS
approved