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

1,3

Comments

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

Links

Table of n, a(n) for n=1..111.

Example

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

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 *)

Prog

(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.
(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

Crossrefs

Cf. A088886, A075002.

Sequence in context: A318879 A333783 A088886 * A305566 A326813 A137347

Adjacent sequences: A317633 A317634 A317635 * A317637 A317638 A317639

Keyword

nonn,base

Author

Martins Opmanis, Aug 02 2018

Status

approved