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A245680 Numbers x whose digits can be permuted to produce a multiple of x. 3
1035, 1089, 1359, 1386, 1782, 2178, 2475, 10035, 10089, 10350, 10449, 10890, 10899, 10989, 11688, 11883, 12375, 12903, 13029, 13359, 13449, 13590, 13599, 13659, 13860, 13986, 14085, 14247, 14724, 14859, 15192, 16782, 17604, 17802, 17820, 17832, 17982, 18027 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A008919 is a subset of this sequence.

Every element of the sequence is divisible by 3. - Emmanuel Vantieghem, Oct 27 2015

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

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100

EXAMPLE

A permutation of 1782 is 7128 and 7128 / 1782 = 4.

A permutation of 11688 is 81816 and 81816 / 11688 = 7.

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 print(n); break; fi; od; od; end: P(10^6);

# Alternative:

N:= 100: # to get the first N entries

count:= 0:

for x from 10 while count < N do

  M:= 10^(ilog10(x)+1)-1;

  L:= sort(convert(x, base, 10));

  for i from 2 to floor(M/x) do

    Lp:= sort(convert(i*x, base, 10));

    if Lp = L then

      count:= count+1;

      A[count]:= x;

      break;

    fi

   od

od:

seq(A[i], i=1..count); # Robert Israel, Jul 29 2014

MATHEMATICA

fQ[n_] := AnyTrue[Rest[FromDigits /@ Permutations[IntegerDigits@ n]], Divisible[#, n] &]; Select[Range@ 20000, fQ] (* Michael De Vlieger, Oct 27 2015, Version 10 *)

PROG

(Python)

import itertools

from itertools import permutations

for n in range(1, 10**5):

..plist = list(permutations(str(n)))

..for i in plist:

....num = ''

....for j in range(len(i)):

......num += i[j]

....if int(num)%n==0 and int(num)/n > 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++; break)); if(p>0, print1(n, ", "))) \\ quicker program Derek Orr, Jul 29 2014

CROSSREFS

Cf. A008919, A096092, A096093, A245682.

Sequence in context: A031609 A236804 A023063 * A241787 A175692 A023087

Adjacent sequences:  A245677 A245678 A245679 * A245681 A245682 A245683

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Jul 29 2014

STATUS

approved

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Last modified May 14 16:23 EDT 2021. Contains 343884 sequences. (Running on oeis4.)