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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
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
Sequence in context: A031609 A236804 A023063 * A241787 A175692 A023087
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jul 29 2014
STATUS
approved

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Last modified May 27 23:57 EDT 2024. Contains 372900 sequences. (Running on oeis4.)