A078218 Smallest multiple of n that begins with the concatenation of the divisors of n (in increasing order).

1, 12, 132, 124, 15, 1236, 175, 1248, 1395, 12510, 1111, 12346128, 1131, 127148, 13515, 124816, 1173, 12369186, 1197, 12451020, 137214, 12112210, 12305, 1234681224, 1525, 1213264, 1392714, 1247142820, 12905, 12356101530, 13113

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The concatenation of the divisors of 7 is 17; 175 = 25*7 is the smallest multiple of 7 that begins with 17, so a(7) = 175.

Maple

cdiv:= proc(n) local D, R, j;
  D:= sort(convert(numtheory:-divisors(n), list));
  R:= D[1];
  for j from 2 to nops(D) do
    R:= R * 10^(1+ilog10(D[j])) + D[j];
  od;
  R
end proc:
f:= proc(n) local t, i, r;
  t:= cdiv(n);
  for i from 0 do
    r:= n * ceil(t*10^i/n);
    if r < (t+1)*10^i then return r fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Oct 07 2024

Prog

(PARI) {for(n=1, 31, k=floor(log(n)/log(10))+1; d=divisors(n); v=Str(); for(i=1, matsize(d)[2], v=concat(v, Str(d[i]))); s=eval(v); t=s+1; m=floor(log(s)/log(10))+1; d=k-m; s=s*10^d; t=t*10^d; b=1; while(b>0, q=floor(s/n); while(b>0&&(p=q*n)<t, if(p>=s, print1(p, ", "); b=0, q++)); s=10*s; t=10*t))}

Crossrefs

Cf. A037278, A069872, A078810.

Sequence in context: A160962 A097783 A260018 * A305261 A048643 A111085

Adjacent sequences: A078215 A078216 A078217 * A078219 A078220 A078221

Keyword

base,nonn,look

Author

Amarnath Murthy, Nov 22 2002

Extensions

Edited and extended by Klaus Brockhaus, Dec 06 2002

Status

approved