A112891 a(n) is the least positive integer in base 10 containing n ones that is divisible by n.

1, 110, 111, 11112, 111110, 1111110, 11101111, 111111112, 111111111, 11111111110, 111111111111, 1111111111116, 11111111111113, 111111111111112, 1111111111111110, 111111111111110112, 111101111111111111, 1111111111111111110, 11111111111110111111, 1111111111111111111100, 1111011111111111111111

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..215

Formula

a(n) = n*A112892(n).

Example

a(4) = 11112 because 11112 contains 4 ones and is divisible by 4.

Maple

f:= proc(n) local x, L, i, j, i1, j1, i2, j2;
      if n mod 10 = 0 then return f0(n)
      elif n mod 5 = 0 then return f5(n)
      fi;    x:= (10^n-1)/9;
      if x mod n = 0 then return x fi;
      L:= sort([seq(seq((10^(n+1)-1)/9 + i*10^j, i=`if`(j=n, 0, -1) .. 8), j=0..n)]);
      for x in L do if x mod n = 0 then return x fi od;
      L:= sort([seq(seq(seq(seq((10^(n+2)-1)/9 + i1*10^j1 + i2*10^j2, i1=`if`(j1=n+1, 0, -1)..8), j1=j2+1..n+1), i2=-1..8), j2=0..n)]);
      for x in L do if x mod n = 0 then return x fi od;
      FAIL
end proc:
f0:=  proc(n) local x, L, i, j, i1, j1, i2, j2;
      x:= (10^n-1)*10/9;
      if x mod n = 0 then return x fi;
      L:= sort(10*[seq(seq((10^(n+1)-1)/9 + i*10^j, i=`if`(j=n, 0, -1) .. 8), j=0..n)]);
      for x in L do if x mod n = 0 then return x fi od;
      L:= sort(10*[seq(seq(seq(seq((10^(n+2)-1)/9 + i1*10^j1 + i2*10^j2, i1=`if`(j1=n+1, 0, -1)..8), j1=j2+1..n+1), i2=-1..8), j2=0..n)]);
      for x in L do if x mod n = 0 then return x fi od;
      FAIL
end proc:
f5:=  proc(n) local x, L, i, j, i1, j1, i2, j2;
      x:= (10^n-1)*10/9;
      if x mod n = 0 then return x fi;
      if x + 5 mod n = 0 then return x + 5 fi;
      L:= sort(10*[seq(seq((10^(n+1)-1)/9 + i*10^j, i=`if`(j=n, 0, -1) .. 8), j=0..n)]);
      for x in L do if x mod n = 0 then return x elif x + 5 mod n = 0 then return x + 5 fi od;
      L:= sort(10*[seq(seq(seq(seq((10^(n+2)-1)/9 + i1*10^j1 + i2*10^j2, i1=`if`(j1=n+1, 0, -1)..8), j1=j2+1..n+1), i2=-1..8), j2=0..n)]);
      for x in L do if x mod n = 0 then return x  elif x + 5 mod n = 0 then return x + 5 fi od;
      FAIL
end proc:
map(f, [$1..25]); # Robert Israel, May 28 2025

Crossrefs

Cf. A112889-A112898, A112900-A112905, A112907-A112910.

Sequence in context: A282657 A287138 A288769 * A182621 A267254 A387199

Adjacent sequences: A112888 A112889 A112890 * A112892 A112893 A112894

Keyword

base,nonn

Author

Ray G. Opao, Oct 05 2005

Extensions

Extended by Ray Chandler, Oct 09 2005

More terms from Robert Israel, May 28 2025

Status

approved