A081927 n-th positive integer whose digits sum up to n.

1, 11, 21, 31, 41, 51, 61, 71, 81, 109, 137, 165, 193, 257, 294, 376, 467, 567, 676, 785, 894, 1399, 1778, 1986, 2887, 3869, 4869, 5878, 6887, 7896, 8959, 9968, 18798, 26998, 35999, 45999, 56899, 66989, 76998, 87799, 97889, 178899, 199798, 298988, 398988

Offset: 1

Author

Amarnath Murthy, Apr 01 2003

Keywords

• base
• nonn

Examples

			31 is the 4th integer of the sequence and the 4th number whose digits sum up to 4 : 4, 13, 22, [31], 103, 112, 121, 130, ...
109 is the 10th integer of the sequence and the 10th number whose digits sum up to 10 : 19, 28, 37, 46, 55, 64, 73, 82, 91, [109], 118, 127, 136, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..8989

Crossrefs

Leading diagonal of A081926.

Cf. A081928, A181178

Programs

Maple

f:= proc(n) local Res, d, v, count;
    count:= 0;
    for d from ceil(n/9) while count < n do
       v:= g(n,d,n-count,1);
       Res:= v[-1];
       count:= count + nops(v);
    od:
    Res
end proc:
g:= proc(n,d,remain) local rem, Res, j, j0, v;
      if remain = 0 then return [] else rem:= remain fi;
      if nargs = 4 then j0:= 1 else j0:= 0 fi;
      if d = 1 then if n >= j0 and n <= 9 then [n] else [] fi
      else
        Res:= NULL;
        for j from max(j0, ceil(n-9*(d-1))) to min(9,n) while rem > 0 do
          v:= map(t -> j*10^(d-1)+t, procname(n-j,d-1,rem));
          Res:= Res, op(v);
          rem:= rem - nops(v);
        od;
        [Res]
      fi
end proc:
map(f, [$1..200]); # Robert Israel, Feb 19 2018

Mathematica

Table[Select[Range[500000],Total[IntegerDigits[#]]==n&][[n]],{n,45}] (* Harvey P. Dale, Mar 02 2024 *)

Formula

From Robert Israel, Feb 20 2018: (Start)

a(9*k-j) = (12-j)*10^(k-1) - 10^(k-10) - 10^(j+k-45) - 1 for j=2..9, k >= 45-j.

a(9*k-1) = 2*10^k - 10^(k-9) - 10^(k-35) - 1, k >= 35. (End)

Extensions

Corrected and extended by Ray Chandler, Oct 29 2003