A069525 Smallest multiple of n with digit sum = 6, or 0 if no such number exists, e.g. a(9k)= 0.

6, 6, 6, 24, 15, 6, 42, 24, 0, 60, 33, 24, 312, 42, 15, 240, 51, 0, 114, 60, 42, 132, 1104, 24, 150, 312, 0, 420, 1131, 60, 1023, 2112, 33, 204, 105, 0, 222, 114, 312, 240, 123, 42, 1032, 132, 0, 1104, 141, 240, 12201, 150, 51, 312, 1113, 0, 330, 4200, 114, 4002, 2301

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• base
• nonn

Comments

In addition to those divisible by 9, all numbers n divisible by 239, 271 or 803 have a(n)=0. - Robert Israel, Sep 04 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A062220, A069521, A069522, A069523, A069524.

Programs

Maple

N:= 1000: # to get a(1)..a(N)
nextL:= proc(L)
local m,q,Lp;
for m from 1 do
   if L[m] > 0 then
    if m = LinearAlgebra:-Dimension(L) then return <5,0$(m-1),1>
    else Lp:= L;
       Lp[1]:= L[m]-1;
       Lp[2..m]:= 0;
       Lp[m+1]:= L[m+1]+1;
       return Lp;
    fi
   fi
od;
end proc:
nogo:= proc(n) local m,a2,a5,S,S2,S3,i,j;
  a2:= padic:-ordp(n,2);
  a5:= padic:-ordp(n,5);
  m:= numtheory:-order(10,n/(2^a2*5^a5))+max(a2,a5);
  S:= {seq(10^i mod n, i=0..m-1)};
  S2:= {seq(seq(S[i]+S[j] mod n,j=1..i),i=1..nops(S))};
  S3:= {seq(seq(S[i]+ S2[j] mod n, j=1..nops(S2)),i=1..nops(S))};
  evalb(S3 intersect map(t -> -t mod n, S3) = {});
end proc:
Agenda:= remove(t -> (t mod 9=0 or t mod 239=0 or t mod 271=0 or t mod 803=0, {$1..N}):
L:= <6>: x:= 6:
A:= Vector(N):
while Agenda <> {} and x < 10^20 do
  x:= add(L[i]*10^(i-1),i=1..LinearAlgebra:-Dimension(L));
  found,Agenda:= selectremove(t -> x mod t = 0, Agenda);
  if found <> {} then
    A[convert(found,list)]:= x;
  fi;
  L:= nextL(L);
od:
Agenda:= remove(nogo,Agenda);
if Agenda <> {} then printf("Values not found for %a\n",Agenda) fi;
convert(A,list); # Robert Israel, Sep 04 2019

Mathematica

Array[If[AnyTrue[Mod[#, {9, 239, 271, 803}], # == 0 &], 0, Block[{k = 1}, While[Total@ IntegerDigits[k #] != 6, k++]; k #]] &, 59] (* Michael De Vlieger, Sep 04 2019 *)

Formula

a(n) = n*A088395(n). - R. J. Mathar, Aug 06 2019

Extensions

More terms from Ray Chandler, Jul 30 2003