A078283 a(1) = 1, a(n) is the smallest multiple of n which is obtained by inserting/prefixing or suffixing at least one digit in a(n-1).

1, 10, 102, 1012, 10120, 101202, 1012025, 10120256, 101120256, 1011202560, 10112002560, 100112002560, 1001120025360, 10010120025360, 100010120025360, 1000010120025360, 10000101020025360, 100001010200253606

Offset: 1

Author

Amarnath Murthy, Nov 25 2002

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A078282, A078284.

Programs

Maple

f:= proc(m,n)
 local L,nL,d,r,K,Kp,tmin,t,V,Vt,x;
 L:= convert(m,base,10);
 nL:= nops(L);
 L:= Vector(L);
 for d from 1 do
   r:= infinity;
   V:= Vector(nL+d);
   for K in combinat:-choose(nL+d,nL) do
     V[K]:= L;
     Kp:= sort(convert({$1..nL+d} minus convert(K,set), list));
     if Kp[-1] = nL+d then tmin:= 10^(d-1) else tmin:= 0 fi;
     for t from tmin to 10^d-1 do
       Vt:= convert(10^d+t,base,10);
       V[Kp]:= Vector(Vt[1..-2]);
       x:= add(10^(i-1)*V[i],i=1..nL+d);
       if x > r then break fi;
       if x mod n = 0 then r:= x; break fi;
     od;
   od;
   if r < infinity then return r fi
 od;
end proc:
A[1]:= 1:
for n from 2 to 30 do A[n]:= f(A[n-1],n) od:
seq(A[i],i=1..30); # Robert Israel, Jul 21 2020

Extensions

More terms from Sascha Kurz, Jan 04 2003