A096686 - OEIS

%I #15 Sep 25 2024 18:35:51

%S 7,35,259,175,14,1295,1,875,86419753,7,7,6475,539,5,518,4375,4571,

%T 432098765,4053,35,37,35,33509,32375,28,2695,285473251,25,265783,259,

%U 25067,21875,23569,22855,2,2160493825,21,20265,1813,175,1897,185,179249

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

%H Robert Israel, <a href="/A096686/b096686.txt">Table of n, a(n) for n = 1..10000</a>

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

%p f:= proc(n)  local q, q2, q5, n1, R, Agenda,d, newA, t, t1, t2;

%p q2:= padic:-ordp(n,2);

%p q5:= padic:-ordp(n,5);

%p q:= max(q2,q5);

%p n1:= n/2^q2/5^q5;

%p R[7]:= 7: Agenda:= {7}:

%p if 7 mod n1 = 0 then return 10^q*7/n fi;

%p for d from 2 do

%p     newA:= NULL;

%p     for t in Agenda do

%p       t1:= 10*t mod n1;

%p       if not assigned(R[t1]) then

%p         R[t1]:= 10*R[t];

%p         newA:= newA, t1;

%p       fi;

%p       t2:= (10*t+7) mod n1;

%p       if t2 = 0 then

%p         return 10^q*(10*R[t]+7)/n;

%p         break

%p       elif not assigned(R[t2]) then

%p         R[t2]:= 10*R[t]+7;

%p         newA:= newA,t2;

%p       fi;

%p     od;

%p     Agenda:= [newA];

%p od:

%p end proc:

%p map(f, [$1..50]); # _Robert Israel_, Mar 06 2017

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

%K base,nonn,look

%O 1,1

%A _Ray Chandler_, Jul 12 2004