A069524 Smallest multiple of n with digit sum = 5, or 0 if no such number exists, e.g. a(3k) = a(11k) = 0.

5, 14, 0, 32, 5, 0, 14, 32, 0, 50, 0, 0, 104, 14, 0, 32, 221, 0, 1121, 140, 0, 0, 23, 0, 50, 104, 0, 140, 203, 0, 2201, 32, 0, 2210, 140, 0, 0, 3002, 0, 320, 41, 0, 2021, 0, 0, 230, 2021, 0, 22001, 50, 0, 104, 212, 0, 0, 1400, 0, 2030, 1121, 0, 122, 22010, 0, 320, 1040

Offset: 1

Author

Amarnath Murthy, Apr 01 2002

Keywords

• base
• nonn

Comments

a(3k)= a(11k) =a(37k)=0. - Ray Chandler, Jul 30 2003

Links

• Robert Israel, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A052219, A069521, A069522, A069523.

Programs

Maple

nextL:= proc(L)
 local m,q,Lp;
 for m from 1 do
   if L[m] > 0 then
    if m = LinearAlgebra:-Dimension(L) then return <4,0$(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:
N:= 300:
Agenda:= remove(t -> ormap(s -> (t mod s = 0), [3,11,37,101,137,239]), {$1..N}):
L:= <5>: x:= 5:
A:= Vector(N):
while Agenda <> {} and x < 10^40 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:
convert(A,list): # Robert Israel, Sep 05 2019

Mathematica

Table[If[MemberQ[Table[Mod[n,q],{q,{3,11,37,101,137,239}}],0],0,With[{k=5000},SelectFirst[n*Range[k],Total[IntegerDigits[#]] == 5&]]],{n,70}] (* Harvey P. Dale, Nov 03 2024 *)

Formula

a(n) = n*A088394(n). - R. J. Mathar, Aug 06 2019

Extensions

More terms from Ray Chandler, Jul 30 2003