A317636 Minimum number of consecutive positive integers starting with 1 that must be concatenated in descending order so that n divides the concatenation, or zero if n divides no such concatenation.

1, 0, 2, 0, 0, 0, 2, 0, 8, 0, 14, 0, 15, 0, 0, 0, 9, 0, 5, 0, 2, 0, 16, 0, 0, 0, 26, 0, 4, 0, 25, 0, 14, 0, 0, 0, 21, 0, 15, 0, 40, 0, 67, 0, 0, 0, 78, 0, 54, 0, 9, 0, 66, 0, 0, 0, 5, 0, 25, 0, 111, 0, 44, 0, 0, 0, 161, 0, 18, 0, 49, 0, 30, 0, 0, 0, 73, 0, 15, 0, 27, 0, 27, 0, 0, 0, 41, 0, 20, 0, 54, 0, 47, 0, 0, 0, 63, 0, 18, 0, 98, 0, 102, 0, 0, 0, 3, 0, 99, 0, 21

Offset: 1

Author

Martins Opmanis, Aug 02 2018

Keywords

• nonn
• base

Comments

a(n) = 0 if n is even or a multiple of 5. Empirical observation: a(n) > 0 for all other n values.

Examples

			For n=19 the a(19)=5 since 54321 = 19*2859, while 4321, 321, 21 and 1 are not multiples of 19.
		

Crossrefs

Cf. A088886, A075002.

Programs

Mathematica

Table[If[GCD[n, 10] == 1, Block[{k = 1}, While[Mod[FromDigits@ Flatten@ Map[IntegerDigits, Range[k, 1, -1]], n] != 0, k++]; k],0], {n, 111}] (* Michael De Vlieger, Aug 02 2018 *)

PARI

a(n) = {if ((n%2) && (n%5), my(s = ""); for (k=1, oo, s = concat(Str(k), s); if (!(eval(s) % n), return (k)););); return (0);} \\ Michel Marcus, Aug 02 2018

Pascal

program skaitlirinda2;
var i : longint;
function Atrodi(n : longint) : int64;
var sk, koefa, naksk, rez : int64;
begin
   sk := 1;
   naksk := 10;
   koefa := naksk mod n;
   rez := sk mod n;
   while rez>0 do
    begin
     Inc(sk);
     rez := (sk * koefa + rez) mod n;
     if sk=naksk then naksk := naksk * 10;
     koefa := (koefa*naksk) mod n;
    end;
   Atrodi := sk;
end;
begin
  for i:=1 to 10000 do
   begin
    if (i mod 2)*(i mod 5) > 0 then writeln(i,' ',Atrodi(i)) else writeln(i,' 0');
   end;
end.