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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).

%I A078283 #9 Jul 22 2020 02:18:44
%S A078283 1,10,102,1012,10120,101202,1012025,10120256,101120256,1011202560,
%T A078283 10112002560,100112002560,1001120025360,10010120025360,
%U A078283 100010120025360,1000010120025360,10000101020025360,100001010200253606
%N 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).
%H A078283 Robert Israel, <a href="/A078283/b078283.txt">Table of n, a(n) for n = 1..210</a>
%p A078283 f:= proc(m,n)
%p A078283  local L,nL,d,r,K,Kp,tmin,t,V,Vt,x;
%p A078283  L:= convert(m,base,10);
%p A078283  nL:= nops(L);
%p A078283  L:= Vector(L);
%p A078283  for d from 1 do
%p A078283    r:= infinity;
%p A078283    V:= Vector(nL+d);
%p A078283    for K in combinat:-choose(nL+d,nL) do
%p A078283      V[K]:= L;
%p A078283      Kp:= sort(convert({$1..nL+d} minus convert(K,set), list));
%p A078283      if Kp[-1] = nL+d then tmin:= 10^(d-1) else tmin:= 0 fi;
%p A078283      for t from tmin to 10^d-1 do
%p A078283        Vt:= convert(10^d+t,base,10);
%p A078283        V[Kp]:= Vector(Vt[1..-2]);
%p A078283        x:= add(10^(i-1)*V[i],i=1..nL+d);
%p A078283        if x > r then break fi;
%p A078283        if x mod n = 0 then r:= x; break fi;
%p A078283      od;
%p A078283    od;
%p A078283    if r < infinity then return r fi
%p A078283  od;
%p A078283 end proc:
%p A078283 A[1]:= 1:
%p A078283 for n from 2 to 30 do A[n]:= f(A[n-1],n) od:
%p A078283 seq(A[i],i=1..30); # _Robert Israel_, Jul 21 2020
%Y A078283 Cf. A078282, A078284.
%K A078283 base,nonn
%O A078283 1,2
%A A078283 _Amarnath Murthy_, Nov 25 2002
%E A078283 More terms from _Sascha Kurz_, Jan 04 2003