A088886 -id:A088886 - cp's OEIS frontend

A088885 Minimum number of consecutive previous nonnegative integers to n that must be concatenated together in descending order such that n divides the concatenated term, or zero if n divides no such concatenation.

1, 2, 2, 2, 5, 2, 0, 6, 8, 10, 0, 6, 0, 8, 5, 4, 2, 8, 3, 0, 0, 10, 0, 12, 0, 0, 26, 16, 0, 20, 0, 20, 11, 2, 20, 8, 0, 0, 0, 20, 40, 20, 4, 32, 35, 46, 38, 20, 40, 0, 2, 0, 0, 26, 10, 20, 3, 0, 0, 20, 55, 0, 0, 52, 0, 32, 0, 44, 17, 20, 0, 36, 26, 0, 50, 52, 21, 38, 67, 20, 0, 0, 9, 20, 0, 4, 59

Offset: 1

Chuck Seggelin, Oct 29 2003

Concatenation always begins at n-1 and cannot go further than n-n (zero). Hence the maximum value of a(n) is n.

			a(8) = 6 because will divide the number formed by concatenating the 6 integers prior to 8 in descending order (i.e. 765432). 8 will not divide any lesser number of previous terms concatenated together beginning with 7 (i.e. 8 will not divide 7, 76, 765, 7654, or 76543). a(7) = 0 because 7 will not divide 6, 65, 654, 6543, 65432, 654321, or 6543210.

Cf. A088798, A088800, A088869, A088871, A088886.

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.

Original entry on oeis.org

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

Martins Opmanis, Aug 02 2018

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

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

Cf. A088886, A075002.

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 *)

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

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.

cp's OEIS Frontend

A088885 Minimum number of consecutive previous nonnegative integers to n that must be concatenated together in descending order such that n divides the concatenated term, or zero if n divides no such concatenation.

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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.

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Mathematica

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Pascal