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

%I A096686 #15 Sep 25 2024 18:35:51
%S A096686 7,35,259,175,14,1295,1,875,86419753,7,7,6475,539,5,518,4375,4571,
%T A096686 432098765,4053,35,37,35,33509,32375,28,2695,285473251,25,265783,259,
%U A096686 25067,21875,23569,22855,2,2160493825,21,20265,1813,175,1897,185,179249
%N A096686 Least k such that decimal representation of k*n contains only digits 0 and 7.
%H A096686 Robert Israel, <a href="/A096686/b096686.txt">Table of n, a(n) for n = 1..10000</a>
%F A096686 a(n) = A078246(n)/n.
%p A096686 f:= proc(n)  local q, q2, q5, n1, R, Agenda,d, newA, t, t1, t2;
%p A096686 q2:= padic:-ordp(n,2);
%p A096686 q5:= padic:-ordp(n,5);
%p A096686 q:= max(q2,q5);
%p A096686 n1:= n/2^q2/5^q5;
%p A096686 R[7]:= 7: Agenda:= {7}:
%p A096686 if 7 mod n1 = 0 then return 10^q*7/n fi;
%p A096686 for d from 2 do
%p A096686     newA:= NULL;
%p A096686     for t in Agenda do
%p A096686       t1:= 10*t mod n1;
%p A096686       if not assigned(R[t1]) then
%p A096686         R[t1]:= 10*R[t];
%p A096686         newA:= newA, t1;
%p A096686       fi;
%p A096686       t2:= (10*t+7) mod n1;
%p A096686       if t2 = 0 then
%p A096686         return 10^q*(10*R[t]+7)/n;
%p A096686         break
%p A096686       elif not assigned(R[t2]) then
%p A096686         R[t2]:= 10*R[t]+7;
%p A096686         newA:= newA,t2;
%p A096686       fi;
%p A096686     od;
%p A096686     Agenda:= [newA];
%p A096686 od:
%p A096686 end proc:
%p A096686 map(f, [$1..50]); # _Robert Israel_, Mar 06 2017
%t A096686 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 *)
%Y A096686 Cf. A004290, A078241-A078248, A079339, A096681-A096688.
%K A096686 base,nonn,look
%O A096686 1,1
%A A096686 _Ray Chandler_, Jul 12 2004