login
A081927
n-th positive integer whose digits sum up to n.
5
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
1,2
LINKS
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)
EXAMPLE
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, ...
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 *)
CROSSREFS
Leading diagonal of A081926.
Sequence in context: A061589 A110402 A330286 * A181178 A178205 A239464
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Apr 01 2003
EXTENSIONS
Corrected and extended by Ray Chandler, Oct 29 2003
STATUS
approved