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%I #26 Aug 08 2014 18:24:54
%S 123876,142857,153846,230769,285714,1028574,1218753,1238760,1239876,
%T 1246878,1294857,1402857,1420785,1425897,1428507,1428570,1428597,
%U 1428705,1429857,1485792,1492857,1538460,1539846,1570284,1584297,2300769,2307690,2307699,2309769,2857014,2857140,2859714,2985714,10028574,10178649
%N Numbers x whose digits can be permuted to produce more than a single multiple of x.
%C It is a subset of A245680.
%C If x < 10^d is in the sequence, then so are x*10^j*(1+10^d+...+10^k*d) for all nonnegative integers j and k. - _Robert Israel_, Jul 29 2014
%H Paolo P. Lava, <a href="/A245682/b245682.txt">Table of n, a(n) for n = 1..200</a>
%e Two permutations of 123876 are 371628, 867132 and 371628 / 123876 = 3, 867132 / 123876 = 7.
%e Five permutations of 142857 are 285714, 428571, 571428, 714285, 857142 and 285714 / 142857 = 2, 428571 / 142857 = 3, 571428 / 142857 = 4, 714285 / 142857 = 5, 857142 / 142857 = 6.
%p P:=proc(q) local a,b,c,i,j,k,n,t; for n from 1 to q do a:=n; b:=[];
%p while a>0 do b:=[a mod 10,op(b)]; a:=trunc(a/10); od;
%p t:=0; for i from 2 to 9 do a:=i*n; c:=[];
%p while a>0 do c:=[a mod 10,op(c)]; a:=trunc(a/10); od;
%p if sort(b)=sort(c) then t:=t+1; fi; if t>1 then print(n); break;
%p fi; od; od; end: P(10^10);
%p # Alternative
%p N:= 10: # get a(1) to a(N)
%p count:= 0:
%p for x from 10 while count < N do
%p M:= 10^(ilog10(x)+1)-1;
%p L:= sort(convert(x,base,10));
%p mults:= 0;
%p for i from 2 to floor(M/x) do
%p Lp:= sort(convert(i*x,base,10));
%p if Lp = L then
%p mults:= mults+1;
%p if mults = 2 then
%p count:= count+1;
%p A[count]:= x;
%p print(x);
%p break;
%p fi
%p fi
%p od
%p od:
%p seq(A[i],i=1..count); # _Robert Israel_, Jul 29 2014
%o (Python)
%o import itertools
%o from itertools import permutations
%o for n in range(1,10**8):
%o ..plist = list(permutations(str(n)))
%o ..count = 0
%o ..lst = []
%o ..for i in plist:
%o ....num = ''
%o ....for j in range(len(i)):
%o ......num += i[j]
%o ....if int(num)%n==0 and int(num)/n > 1:
%o ......if int(num) not in lst:
%o ........lst.append(int(num))
%o ........count += 1
%o ..if count > 1:
%o ....print(n,end=', ') # _Derek Orr_, Jul 29 2014
%o (PARI)
%o for(n=1,10^8,d=vecsort(digits(n));p=0;for(k=2,9,dd=vecsort(digits(n*k));if(d==dd,p++));if(p>1,print1(n,", "))) \\ faster program _Derek Orr_, Jul 29 2014
%Y Cf. A008919, A096092, A096093, A245680.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Jul 29 2014
%E a(7) to a(10) from _Robert Israel_, Jul 29 2014
%E a(11) - a(35) from _Derek Orr_, Jul 29 2014
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