A245682 Numbers x whose digits can be permuted to produce more than a single multiple of x.

123876, 142857, 153846, 230769, 285714, 1028574, 1218753, 1238760, 1239876, 1246878, 1294857, 1402857, 1420785, 1425897, 1428507, 1428570, 1428597, 1428705, 1429857, 1485792, 1492857, 1538460, 1539846, 1570284, 1584297, 2300769, 2307690, 2307699, 2309769, 2857014, 2857140, 2859714, 2985714, 10028574, 10178649

Offset

1,1

Comments

It is a subset of A245680.

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

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Example

Two permutations of 123876 are 371628, 867132  and  371628 / 123876 = 3, 867132  / 123876 = 7.
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.

Maple

P:=proc(q) local a, b, c, i, j, k, n, t; for n from 1 to q do a:=n; b:=[];
while a>0 do b:=[a mod 10, op(b)]; a:=trunc(a/10); od;
t:=0; for i from 2 to 9 do a:=i*n; c:=[];
while a>0 do c:=[a mod 10, op(c)]; a:=trunc(a/10); od;
if sort(b)=sort(c) then t:=t+1; fi; if t>1 then print(n); break;
fi; od; od; end: P(10^10);
# Alternative
N:= 10: # get a(1) to a(N)
count:= 0:
for x from 10 while count < N do
  M:= 10^(ilog10(x)+1)-1;
  L:= sort(convert(x, base, 10));
  mults:= 0;
  for i from 2 to floor(M/x) do
    Lp:= sort(convert(i*x, base, 10));
    if Lp = L then
      mults:= mults+1;
      if mults = 2 then
        count:= count+1;
        A[count]:= x;
        print(x);
        break;
      fi
    fi
   od
od:
seq(A[i], i=1..count); # Robert Israel, Jul 29 2014

Prog

(Python)
import itertools
from itertools import permutations
for n in range(1, 10**8):
..plist = list(permutations(str(n)))
..count = 0
..lst = []
..for i in plist:
....num = ''
....for j in range(len(i)):
......num += i[j]
....if int(num)%n==0 and int(num)/n > 1:
......if int(num) not in lst:
........lst.append(int(num))
........count += 1
..if count > 1:
....print(n, end=', ') # Derek Orr, Jul 29 2014
(PARI)
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

Crossrefs

Cf. A008919, A096092, A096093, A245680.

Sequence in context: A371845 A209734 A049358 * A237322 A205655 A206184

Adjacent sequences: A245679 A245680 A245681 * A245683 A245684 A245685

Keyword

nonn,base

Author

Paolo P. Lava, Jul 29 2014

Extensions

a(7) to a(10) from Robert Israel, Jul 29 2014

a(11) - a(35) from Derek Orr, Jul 29 2014

Status

approved