A096686 Least k such that decimal representation of k*n contains only digits 0 and 7.

7, 35, 259, 175, 14, 1295, 1, 875, 86419753, 7, 7, 6475, 539, 5, 518, 4375, 4571, 432098765, 4053, 35, 37, 35, 33509, 32375, 28, 2695, 285473251, 25, 265783, 259, 25067, 21875, 23569, 22855, 2, 2160493825, 21, 20265, 1813, 175, 1897, 185, 179249

Offset: 1

Author

Ray Chandler, Jul 12 2004

Keywords

• base
• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004290, A078241-A078248, A079339, A096681-A096688.

Programs

Maple

f:= proc(n)  local q, q2, q5, n1, R, Agenda,d, newA, t, t1, t2;
q2:= padic:-ordp(n,2);
q5:= padic:-ordp(n,5);
q:= max(q2,q5);
n1:= n/2^q2/5^q5;
R[7]:= 7: Agenda:= {7}:
if 7 mod n1 = 0 then return 10^q*7/n fi;
for d from 2 do
    newA:= NULL;
    for t in Agenda do
      t1:= 10*t mod n1;
      if not assigned(R[t1]) then
        R[t1]:= 10*R[t];
        newA:= newA, t1;
      fi;
      t2:= (10*t+7) mod n1;
      if t2 = 0 then
        return 10^q*(10*R[t]+7)/n;
        break
      elif not assigned(R[t2]) then
        R[t2]:= 10*R[t]+7;
        newA:= newA,t2;
      fi;
    od;
    Agenda:= [newA];
od:
end proc:
map(f, [$1..50]); # Robert Israel, Mar 06 2017

Mathematica

f07[n_]:=Module[{k=1},While[!SubsetQ[{0,7},IntegerDigits[n*k]],k++];k]; Array[f07,8] (* The program generates the first 8 terms of the sequence. To generate more, increase the Array constant but because some of the terms are quite large the program may take a long time to run. *) (* Harvey P. Dale, Sep 25 2024 *)

Formula

a(n) = A078246(n)/n.