cp's OEIS Frontend

A245680 Numbers x whose digits can be permuted to produce a multiple of x.

%I A245680 #35 May 22 2025 10:21:39
%S A245680 1035,1089,1359,1386,1782,2178,2475,10035,10089,10350,10449,10890,
%T A245680 10899,10989,11688,11883,12375,12903,13029,13359,13449,13590,13599,
%U A245680 13659,13860,13986,14085,14247,14724,14859,15192,16782,17604,17802,17820,17832,17982,18027
%N A245680 Numbers x whose digits can be permuted to produce a multiple of x.
%C A245680 A008919 is a subset of this sequence.
%C A245680 Every element of the sequence is divisible by 3. - _Emmanuel Vantieghem_, Oct 27 2015
%C A245680 It is an obvious fact that if a(n) is the n-th term of the sequence, then a(n)*(10^k) is also a member of the sequence for all k > 0. - _Altug Alkan_, Nov 01 2015
%H A245680 Paolo P. Lava, <a href="/A245680/b245680.txt">Table of n, a(n) for n = 1..100</a>
%e A245680 A permutation of 1782 is 7128 and 7128 / 1782 = 4.
%e A245680 A permutation of 11688 is 81816 and 81816 / 11688 = 7.
%p A245680 P:=proc(q) local a, b, c, i, j, k, n, t; for n from 1 to q do a:=n; b:=[];
%p A245680 while a>0 do b:=[a mod 10, op(b)]; a:=trunc(a/10); od;
%p A245680 t:=0; for i from 2 to 9 do a:=i*n; c:=[];
%p A245680 while a>0 do c:=[a mod 10, op(c)]; a:=trunc(a/10); od;
%p A245680 if sort(b)=sort(c) then print(n); break; fi; od; od; end: P(10^6);
%p A245680 # Alternative:
%p A245680 N:= 100: # to get the first N entries
%p A245680 count:= 0:
%p A245680 for x from 10 while count < N do
%p A245680   M:= 10^(ilog10(x)+1)-1;
%p A245680   L:= sort(convert(x,base,10));
%p A245680   for i from 2 to floor(M/x) do
%p A245680     Lp:= sort(convert(i*x,base,10));
%p A245680     if Lp = L then
%p A245680       count:= count+1;
%p A245680       A[count]:= x;
%p A245680       break;
%p A245680     fi
%p A245680    od
%p A245680 od:
%p A245680 seq(A[i],i=1..count); # _Robert Israel_, Jul 29 2014
%t A245680 fQ[n_] := AnyTrue[Rest[FromDigits /@ Permutations[IntegerDigits@ n]], Divisible[#, n] &]; Select[Range@ 20000, fQ] (* _Michael De Vlieger_, Oct 27 2015, Version 10 *)
%o A245680 (Python)
%o A245680 import itertools
%o A245680 from itertools import permutations
%o A245680 for n in range(1,10**5):
%o A245680   plist = list(permutations(str(n)))
%o A245680   for i in plist:
%o A245680     num = ''
%o A245680     for j in range(len(i)):
%o A245680       num += i[j]
%o A245680     if int(num)%n==0 and int(num)/n > 1:
%o A245680       print(n,end=', ') # _Derek Orr_, Jul 29 2014
%o A245680 (PARI)
%o A245680 for(n=1,10^8,d=vecsort(digits(n));p=0;for(k=2,9,dd=vecsort(digits(n*k));if(d==dd,p++;break));if(p>0,print1(n,", "))) \\ quicker program _Derek Orr_, Jul 29 2014
%Y A245680 Cf. A008919, A096092, A096093, A245682.
%K A245680 nonn,base
%O A245680 1,1
%A A245680 _Paolo P. Lava_, Jul 29 2014