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
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
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
Comments