A075002 -id:A075002 - cp's OEIS frontend

A334620 a(n) is the smallest multiple of n formed by the concatenation 1,2,3,...,k for some k.

1, 12, 12, 12, 12345, 12, 1234567891011, 123456, 12345678, 12345678910, 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106, 12

Offset: 1

Eder Vanzei, Sep 09 2020

			a(3) = 12, because 12 is the smallest multiple of 3 that appears in A007908.

Robert Israel, Table of n, a(n) for n = 1..144

Cf. A007908, A075002.

f:= proc(n) local x,i;
x:= 0;
for i from 1 do
  x:= x*10^(1+ilog10(i))+i;
  if x mod n = 0 then return x fi
od
end proc:
map(f, [$1..20]); # Robert Israel, Oct 25 2020

smn[n_]:=Module[{k=1,c=1},While[!Divisible[c,n],k++;c= c*10^IntegerLength[ k]+ k];c]; Array[ smn,20] (* Harvey P. Dale, Apr 04 2022 *)

a(n) = j="";for(k=1, oo, j=eval(concat(Str(j), k)); if(j%n==0, return(j)))

a(n) is the smallest multiple of n appearing in A007908.

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

A334620 a(n) is the smallest multiple of n formed by the concatenation 1,2,3,...,k for some k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula