cp's OEIS Frontend

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

%I A069524 #14 Nov 03 2024 11:03:06
%S A069524 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,
%T A069524 104,0,140,203,0,2201,32,0,2210,140,0,0,3002,0,320,41,0,2021,0,0,230,
%U A069524 2021,0,22001,50,0,104,212,0,0,1400,0,2030,1121,0,122,22010,0,320,1040
%N A069524 Smallest multiple of n with digit sum = 5, or 0 if no such number exists, e.g. a(3k) = a(11k) = 0.
%C A069524 a(3k)= a(11k) =a(37k)=0. - _Ray Chandler_, Jul 30 2003
%H A069524 Robert Israel, <a href="/A069524/b069524.txt">Table of n, a(n) for n = 1..3000</a>
%F A069524 a(n) = n*A088394(n). - _R. J. Mathar_, Aug 06 2019
%p A069524 nextL:= proc(L)
%p A069524  local m,q,Lp;
%p A069524  for m from 1 do
%p A069524    if L[m] > 0 then
%p A069524     if m = LinearAlgebra:-Dimension(L) then return <4,0$(m-1),1>
%p A069524     else Lp:= L;
%p A069524        Lp[1]:= L[m]-1;
%p A069524        Lp[2..m]:= 0;
%p A069524        Lp[m+1]:= L[m+1]+1;
%p A069524        return Lp;
%p A069524     fi
%p A069524    fi
%p A069524  od;
%p A069524 end proc:
%p A069524 N:= 300:
%p A069524 Agenda:= remove(t -> ormap(s -> (t mod s = 0), [3,11,37,101,137,239]), {$1..N}):
%p A069524 L:= <5>: x:= 5:
%p A069524 A:= Vector(N):
%p A069524 while Agenda <> {} and x < 10^40 do
%p A069524   x:= add(L[i]*10^(i-1),i=1..LinearAlgebra:-Dimension(L));
%p A069524   found,Agenda:= selectremove(t -> x mod t = 0, Agenda);
%p A069524   if found <> {} then
%p A069524     A[convert(found,list)]:= x;
%p A069524   fi;
%p A069524   L:= nextL(L);
%p A069524 od:
%p A069524 convert(A,list): # _Robert Israel_, Sep 05 2019
%t A069524 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 *)
%Y A069524 Cf. A052219, A069521, A069522, A069523.
%K A069524 base,nonn
%O A069524 1,1
%A A069524 _Amarnath Murthy_, Apr 01 2002
%E A069524 More terms from _Ray Chandler_, Jul 30 2003